If x = 5 units, y = 15 units, and h = 8 units, find the area of the parallelogram shown above using decomposition. A. 160 square units B. 80 square units C. 40 square units D. 120 square units
To find the area of the parallelogram shown above, we need to decompose it into two triangles and then calculate the area of each triangle separately.
First, calculate the area of one of the triangles:
Area of a triangle = 1/2 * base * height
Triangle 1:
Base = x = 5 units
Height = y = 15 units
Area of Triangle 1 = 1/2 * 5 * 15 = 37.5 square units
Triangle 2:
Base = x = 5 units
Height = h = 8 units
Area of Triangle 2 = 1/2 * 5 * 8 = 20 square units
Now, add the areas of both triangles to get the total area of the parallelogram:
Total Area = Area of Triangle 1 + Area of Triangle 2
Total Area = 37.5 + 20
Total Area = 57.5 square units
Therefore, the area of the parallelogram shown above using decomposition is 57.5 square units. The closest option is not listed, therefore, the answer is not listed.