Question

1.

(05.01; 05.02 MC)
A parallelogram is shown below:

A parallelogram ABCD is shown with DC equal to 8 feet and the perpendicular distance between AB and DC equal to 3 over 4 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

Part A:

The area of a parallelogram is given by the formula A = base x height. In this case, the base is DC, which is 8 feet, and the height is the perpendicular distance between AB and DC, which is 3/4 foot. Therefore, the area of the parallelogram is:

A = base x height = 8 feet x 3/4 foot = 6 square feet

Part B:

To decompose the parallelogram into two triangles, we can draw a diagonal line from A to C or from B to D, as shown below:

B________C

/ /

/ /

A________D

This diagonal line divides the parallelogram into two congruent triangles, as shown:

B________C

/ | /

/ | /

A_____|__D

|

|

Each triangle has base 4 feet (half of DC) and height 3/4 foot. Therefore, the area of each triangle is:

A = base x height / 2 = 4 feet x 3/4 foot / 2 = 3 square feet.