data_source stringclasses 1 value | prompt listlengths 1 1 | ability stringclasses 1 value | reward_model dict | extra_info dict | level stringclasses 2 values | problem_id stringclasses 2 values |
|---|---|---|---|---|---|---|
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
without-guidance | [
{
"content": "In the diagram, $ABCD$ and $EFGD$ are squares each with side lengths of 5 and 3 respectively, and $H$ is the midpoint of both $BC$ and $EF$. Calculate the total area of the polygon $ABHFGD$.",
"role": "user"
}
] | math | {
"ground_truth": "25.5",
"style": "rule"
} | {
"index": 146,
"split": "without-guidance"
} | easy-without-guidance | easy-93-without-guidance |
without-guidance | [
{
"content": "In parallelogram $ABCD$, $BE$ is the height from vertex $B$ to side $AD$, and segment $ED$ is extended from $D$ such that $ED = 8$. The base $BC$ of the parallelogram is $14$. The entire parallelogram has an area of $126$. Determine the area of the shaded region $BEDC$.",
"role": "user"
}
] | math | {
"ground_truth": "99",
"style": "rule"
} | {
"index": 157,
"split": "without-guidance"
} | easier | easier-413-without-guidance |
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