Question

If x = 8 units, y = 3 units, and h = 10 units, find the area of the trapezoid shown above using decomposition.

A.

110 square units

B.

80 square units

C.

95 square units

D.

140 square units

Answer 1

A = ¹/₂h(b₁ + b₂)
A = ¹/₂(10)(3 + 14)
A = 5(22)
A = 110 units²

The answer is A.

Answer 2

if by decomposition you mean breaking it ino parts then

break it itno 2 triangles and 1 rectangle

left to right

triangle with base y and height h
h=10
y=3
area of traignel=1/2bh
aera=1/2(10)(3)
area=5(3)
area=15

rectangel of legnth x and height h
area=legnth timwe width
x=8
h=10
area=8 times 10
aera=80


last triangle
should be same as other sinces same base (y) and same height (h)
15

add
15+80+15=120