Question
Which of the following models shows why the area of a parallelogram is the same as the area of a rectangle?(1 point)
Responses
An illustration shows a rectangle with a dashed line connecting the bottom left vertex to the opposite side at an angle.
Image with alt text: An illustration shows a rectangle with a dashed line connecting the bottom left vertex to the opposite side at an angle.
An illustration shows a parallelogram with two dashed lines drawn from the top vertices intersecting at the center of the base.
Image with alt text: An illustration shows a parallelogram with two dashed lines drawn from the top vertices intersecting at the center of the base.
An illustration shows a parallelogram with a triangle drawn with dashed lines extending from the base and the right slanting side of the parallelogram.
Image with alt text: An illustration shows a parallelogram with a triangle drawn with dashed lines extending from the base and the right slanting side of the parallelogram.
An illustration shows a parallelogram with two right triangles drawn with dashed lines on either side. A dashed line extends horizontally from the top left and bottom right where they meet dashed vertical lines extending from the bottom left vertex and top right vertex, thus forming triangles on either side.
Responses
An illustration shows a rectangle with a dashed line connecting the bottom left vertex to the opposite side at an angle.
Image with alt text: An illustration shows a rectangle with a dashed line connecting the bottom left vertex to the opposite side at an angle.
An illustration shows a parallelogram with two dashed lines drawn from the top vertices intersecting at the center of the base.
Image with alt text: An illustration shows a parallelogram with two dashed lines drawn from the top vertices intersecting at the center of the base.
An illustration shows a parallelogram with a triangle drawn with dashed lines extending from the base and the right slanting side of the parallelogram.
Image with alt text: An illustration shows a parallelogram with a triangle drawn with dashed lines extending from the base and the right slanting side of the parallelogram.
An illustration shows a parallelogram with two right triangles drawn with dashed lines on either side. A dashed line extends horizontally from the top left and bottom right where they meet dashed vertical lines extending from the bottom left vertex and top right vertex, thus forming triangles on either side.
Answers
GPT-4o mini
The model that shows why the area of a parallelogram is the same as the area of a rectangle is the one that illustrates a parallelogram with two right triangles drawn on either side, where a dashed line extends horizontally from the top left and bottom right, meeting vertical lines extending from the vertices. This model effectively demonstrates how the parallelogram can be transformed into a rectangle by rearranging the triangles, highlighting that both shapes share the same base and height, thus having the same area.