If x = 7 units, y = 3 units, and h = 8 units, find the area of the trapezoid shown above using decomposition.
A.
104 square units
B.
68 square units
C.
56 square units
D.
80 square units
To find the area of the trapezoid, we need to break it down into simple shapes (triangles and rectangles) and then add up their areas.
First, we can split the trapezoid into a rectangle and two right triangles.
The rectangle has a base of 7 units (x) and a height of 8 units (h), so its area is 7 * 8 = 56 square units.
Each right triangle has a base of 3 units (y) and a height of 8 units (h), so the area of each triangle is 0.5 * 3 * 8 = 12 square units.
Since there are two triangles, the total area of the triangles is 2 * 12 = 24 square units.
Therefore, the total area of the trapezoid is 56 (rectangle) + 24 (triangles) = 80 square units.
Therefore, the correct answer is D. 80 square units.