If x = 6 units, y = 7 units, and h = 8 units, find the area of the trapezoid shown above using decomposition.
A.
76 square units
B.
48 square units
C.
160 square units
D.
104 square units
The area of a trapezoid can be found using the formula A = (1/2)(b1 + b2)(h), where b1 and b2 are the lengths of the bases and h is the height.
Given that x = 6 units, y = 7 units, and h = 8 units, we can decompose the trapezoid into a rectangle and two right triangles as shown below:
Rectangle:
Area = x * h = 6 * 8 = 48 square units
Two right triangles:
Each right triangle has a base of 1 unit and a height of 8 units. Since there are two right triangles, the total area is:
2 * (1/2) * 1 * 8 = 8 square units
Total area = Rectangle area + 2 Triangle areas = 48 + 8 = 56 square units
Therefore, the correct answer closest to 56 square units is not provided in the options given.