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 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 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 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 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 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 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 first option is the best representation that shows why the area of a parallelogram is the same as the area of a rectangle.
This option likely illustrates a parallelogram with a triangle drawn with dashed lines extending from the base and the right slanting side of the parallelogram. By moving the triangular section to the opposite side, it can visually demonstrate how the area of the parallelogram can be rearranged to form a rectangle, thereby reinforcing the concept that both shapes hold equal area under certain conditions.
So, if you're selecting based on which model effectively illustrates the equivalence of areas, choose the first illustration.
This option likely illustrates a parallelogram with a triangle drawn with dashed lines extending from the base and the right slanting side of the parallelogram. By moving the triangular section to the opposite side, it can visually demonstrate how the area of the parallelogram can be rearranged to form a rectangle, thereby reinforcing the concept that both shapes hold equal area under certain conditions.
So, if you're selecting based on which model effectively illustrates the equivalence of areas, choose the first illustration.