If x = 8 units, y = 3 units, and h = 10 units, find the area of the trapezoid shown above using decomposition.

Question

A.
80 square units
B.
110 square units
C.
95 square units
D.
140 square units

Answer 1

To find the area of the trapezoid, we need to decompose it into triangles and a rectangle.

First, we can find the area of the rectangle at the bottom of the trapezoid:
Area = x * h = 8 * 10 = 80 square units

Next, we can find the area of the two triangles on the sides of the trapezoid:
Area of each triangle = (1/2) * base * height

For the left triangle:
Area = (1/2) * y * h = (1/2) * 3 * 10 = 15 square units

For the right triangle:
Area = (1/2) * x * h = (1/2) * 8 * 10 = 40 square units

Now, we add the areas of the rectangle and the two triangles to find the total area of the trapezoid:
Total area = 80 + 15 + 40 = 95 square units

Therefore, the area of the trapezoid shown above using decomposition is 95 square units.

Therefore, the correct answer is C. 95 square units.