If x = 4 units, y = 12 units, and h = 9 units, find the area of the parallelogram shown above using decomposition.

Question

A.
36 square units
B.
144 square units
C.
108 square units
D.
72 square units

Answer 1

To find the area of the parallelogram, we can decompose it into two triangles and find the area of each triangle separately.

First, find the base and height of each triangle:
Triangle 1:
Base = x = 4 units
Height = h = 9 units

Area of Triangle 1 = 0.5 * base * height = 0.5 * 4 * 9 = 18 square units

Triangle 2:
Base = y = 12 units
Height = h = 9 units

Area of Triangle 2 = 0.5 * base * height = 0.5 * 12 * 9 = 54 square units

Now, add the areas of both triangles to find the total area of the parallelogram:
Total Area = Area of Triangle 1 + Area of Triangle 2
Total Area = 18 + 54 = 72 square units

Therefore, the area of the parallelogram is 72 square units, which is option D.