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?

Answer 1

Answer:

Part A) Area of Parallelogram:

Area = $Base*Height$

Area = 3 * $\frac{2}{3}$

Area = 2 feet²

Part B)

We can  decompose the parallelogram into two triangle by drawing a diagonal which will divide the parallelogram into two triangles with equal area

Part C)

The area of each triangle would be the half of the area of parallelogram.

=> Area of each triangle = 2 feet²/2 = 1 feet ²

Answer 2

Part A) The area of a parallelogram is base × height.

3 × 2/3 = 6/3 = 2

2 feet squared is the area of the whole parallelogram.

Part B) The diagonal of a parallelogram separates it into two congruent triangles.

The area of each triangle will be:

base × height × 1/2

3 × 2/3 × 1/2 = 6/6 = 1

1 foot squared is the area for each triangle.