Question

A parallelogram is shown below:

A parallelogram ABCD is shown with DC equal to 3 feet and the perpendicular distance between AB and DC equal to 2 over 3 foot.


Part A: What is the area of the parallelogram? Show your work. (5 points)


Part B: How can you decompose this parallelogram into two triangles? If this parallelogram was decomposed into two triangles, what would be the area of each triangle? (5 points)

Answer 1

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Answer:

A. 2 square feet

B. draw a diagonal; 1 square foot

Explanation:

A. The area of a parallelogram is given by the formula ...

A = bh

Here the base (b) is 3 feet, and the height (h) is 2/3 ft. The area is ...

A = (3 ft)(2/3 ft) = 2 ft^2 . . . . area of the parallelogram

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B. Drawing a diagonal (AC or BD) will divide the figure into two congruent triangles. Each triangle has the same base and height as the original parallelogram. The area of one of the triangles is given by ...

A = 1/2bh

Using the given dimensions, ...

A = 1/2(3 ft)(2/3 ft) = 1 ft^2 . . . . area of one triangle