Question

The area of the trapezoid shown is 120 square centimeters. Find the sum of the lengths of the two parallel sides.

A. 12 cm
B. 20 cm
C. 24 cm
D. 30 cm

Answer 1

Its shows to me that it’s D

Answer 2

D

Explanation:

The area formula for a trapezoid is
`A=(b_1+b_2)/(2)*h`, where
`A` is the trapezoid's area,
`b_1` and
`b_2` are the trapezoid's bases, or parallel sides, and
`h` is the trapezoid's height.

We are given that
`A=120`, and from the diagram, we see that
`h=8`. Therefore, all we have to do to find
`b_1+b_2` is substitute the given values into the area formula. Therefore:

`A=(b_1+b_2)/(2)*h`

`120=(b_1+b_2)/(2) *8` (Substitute the given values into the equation)

`120=(b_1+b_2)*4` (Simplify RHS)

`(120)/(4)=((b_1+b_2)*4)/(4)` (Divide both sides of the equation by
`4` to get rid of
`b_1+b_2`'s coefficient)

`b_1+b_2=30` (Simplify, Symmetric Property of Equality)

Hope this helps!