If x = 8 units, y = 3 units, and h = 10 units, find the area of the trapezoid shown above using decomposition.
A.
80 square units
B.
110 square units
C.
95 square units
D.
140 square units
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.