Question

If x = 9 units, y = 3 units, and h = 10 units, find the area of the trapezoid shown above using decomposition.
A.
105 square units
B.
120 square units
C.
90 square units
D.
150 square units

Answer 1

To find the area of the trapezoid using decomposition, we would need to split it into smaller shapes to make it easier to calculate.

First, we can split the trapezoid into a rectangle and a triangle. The rectangle has a height of 3 units and a base of 9 units, so its area is 3 * 9 = 27 square units.

Next, we can calculate the area of the triangle by finding its height and base. The height of the triangle is 7 units (10 units - 3 units), and the base is also 9 units. The area of the triangle is (1/2) * base * height = (1/2) * 9 * 7 = 31.5 square units.

Now, we add the area of the rectangle and the area of the triangle together to find the total area of the trapezoid: 27 + 31.5 = 58.5 square units.

Therefore, the closest option is C. 90 square units.