Question

A parallelogram is shown below:

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

Answer:

2

Step-by-step explanation:

Answer 2

The area of the parallelogram is 8 sq.foot and the area of the triangle is sq.foot.

What is a Parallelogram?

A parallelogram is a polygon with four sides and the opposite sides are parallel.

The base of the side is 9 feet.

The height of the side of (8/9) foot.

From the figure it can be seen that the opposite sides of the base is equal.

The area of a parallelogram is given by,

= ( 1/2) * ( b₁ + b₂) * height

= (1/2) * ( 9 + 9 ) * (8/9)

= 8 sq.foot.

The parallelogram can be decomposed into two triangles along its diagonal BD or AC.

The triangle will be ABD and BCD.

The area of the triangle will be exactly half of the parallelogram.

Area of the triangle can also be determined as,

= (1/2) * base * height

= (1/2) * 9 * 8/9

= 4 sq.foot.

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