Question

If x = 4 units, y = 5 units, and h = 6 units, find the area of the trapezoid shown above using decomposition.
A.
24 square units
B.
39 square units
C.
84 square units
D.
54 square units

Answer 1

To find the area of the trapezoid using decomposition, we need to split the trapezoid into two separate shapes: a rectangle and a triangle.

First, we can see that the two parallel sides of the trapezoid are x and y units long. Using these two sides, we can create a rectangle with a base of 4 units and a height of 5 units, resulting in an area of 4 * 5 = 20 square units.

Next, we can calculate the area of the triangle formed by the height h = 6 units and the difference in the lengths of the parallel sides, which is |x - y| = |4 - 5| = 1 unit. The area of this triangle can be calculated using the formula: 0.5 * base * height = 0.5 * 1 * 6 = 3 square units.

Therefore, to find the total area of the trapezoid, we add the areas of the rectangle and the triangle: 20 + 3 = 23 square units.

Therefore, the closest option to the correct answer is B. 39 square units.