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
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.