If x = 4 units, y = 12 units, and h = 9 units, find the area of the parallelogram shown above using decomposition.
A.
36 square units
B.
144 square units
C.
108 square units
D.
72 square units
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.