Note: Figure is not drawn to scale.
If x = 5 units, y = 15 units, and h = 8 units, find the area of the parallelogram shown above using decomposition.
A.
120 square units
B.
160 square units
C.
40 square units
D.
80 square units
To find the area of the parallelogram using decomposition, we can split it into a rectangle and a right triangle.
First, let's find the area of the rectangle:
The base of the rectangle is x = 5 units and the height is h = 8 units.
Area of rectangle = base * height = 5 * 8 = 40 square units.
Next, let's find the area of the right triangle:
The base of the triangle is y = 15 units and the height is h = 8 units. The right triangle takes up half of the parallelogram, so we can find its area by calculating half of the rectangle area.
Area of triangle = (1/2) * base * height = (1/2) * 15 * 8 = 60 square units.
Therefore, the total area of the parallelogram is the sum of the area of the rectangle and the area of the triangle:
Total area = 40 + 60 = 100 square units.
Therefore, the correct answer is not listed among the options provided.