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
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.