Question

Note: Figure is not drawn to scale.

If x=3 units, y=5 units, and h = 6 units, find the area of the trapezoid shown above using decomposition.

A.
18 square units
B.
33 square units

C. 78 square units

D. 48 square units​

Answer 1

The rectangle area is 18 plus the two triangles are 15 each. So, 15 + 15 = 30. Add them all together 18 + 30 is 48.

The answer is D — 48 square units

Answer 2

D

Explanation:

The trapezoid is composed of a rectangle and 2 congruent right triangles

area of rectangle = xh = 3 × 6 = 18 units²

area of 2 triangles

= 2 ×
`(1)/(2)` yh

= 1 × 5 × 6 = 30 units²

Thus area of trapezoid = 18 + 30 = 48 units² → D