Question

PLEASE HELP!!!!

The formula for the area of a trapezoid is
=12ℎ(1+2)
A=12hb1+b2

, where h is the height and
1
b1

and
2
b2

are the lengths of the two parallel sides.



Based on this formula, which of the following formulas are also true? Select three that apply.

Answer 1

C, D, E

Explanation:

You want to find equations for h and b1 or b2 given the formula for the area of a trapezoid is ...

A = 1/2h(b1 +b2)

Rearrangements

Distributing the factor of 1/2, we get ...

`A=h\left((1)/(2)b_1+(1)/(2)b_2\right)`

Dividing by the coefficient of h, we find ...

`\boxed{h=(A)/(\left((1)/(2)b_1+(1)/(2)b_2\right))}\qquad\text{matches choice E}`

Multiplying the original equation by 2 gives us ...

`2A=h(b_1+b_2)`

From here, we can solve for h or b2 as follows:

`\boxed{h=(2A)/(b_1+b_2)}\qquad\text{divide by the coefficient of h; matches D}\\\\\\\\b_1+b_2=(2A)/(h)\qquad\text{divide by h}\\\\\boxed{b_2=(2A)/(h)-b_1}\qquad\text{subtract $b_1$; matches C}`