Question
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Area of Parallelograms Quick Check
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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 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 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 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.
Image with alt text: 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.
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Area of Parallelograms Quick Check
3 of 53 of 5 Items
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 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 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 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.
Image with alt text: 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.
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Answers
Answered by
GPT-4o mini
To determine which model best demonstrates why the area of a parallelogram is the same as the area of a rectangle, we need to consider the relationships between the shapes.
The area of a parallelogram is calculated using the formula \( \text{Area} = \text{base} \times \text{height} \). This formula applies equally to rectangles, where the height is the perpendicular distance from the base to the top.
Given that, the most suitable model would demonstrate that you can rearrange parts of the parallelogram or visually show how it relates to a rectangle in terms of base and height.
From the options provided, the correct choice is likely:
**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.**
This image likely illustrates how the parallelogram can be transformed into a rectangle by effectively "cutting off" the triangular portions, thus visually showing that the area remains the same when you rearrange the pieces.
The area of a parallelogram is calculated using the formula \( \text{Area} = \text{base} \times \text{height} \). This formula applies equally to rectangles, where the height is the perpendicular distance from the base to the top.
Given that, the most suitable model would demonstrate that you can rearrange parts of the parallelogram or visually show how it relates to a rectangle in terms of base and height.
From the options provided, the correct choice is likely:
**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.**
This image likely illustrates how the parallelogram can be transformed into a rectangle by effectively "cutting off" the triangular portions, thus visually showing that the area remains the same when you rearrange the pieces.