Question

Question
Which correctly shows the area formula for a trapezoid, A=12h(b1+b2)
, rearranged for the quantity of interest h?(1 point)
Responses

h=2Ab1+b2
h equals Start Fraction 2 upper A over b subscript 1 baseline plus b subscript 2 baseline End Fraction

h=b1+b22A
h equals Start Fraction b subscript 1 baseline plus b subscript 2 baseline over 2 upper A End Fraction

h=12A(b1+b2)
h equals Start Fraction 1 over 2 End Fraction upper A left parenthesis b subscript 1 baseline plus b subscript 2 baseline right parenthesis

b1=2Ah−b2

Answer 1

To rearrange the area formula for a trapezoid, \( A = \frac{1}{2}h(b_1 + b_2) \), for the height \( h \), we can follow these steps:

1. Start with the original formula:
\[
A = \frac{1}{2}h(b_1 + b_2)
\]

2. Multiply both sides by 2 to eliminate the fraction:
\[
2A = h(b_1 + b_2)
\]

3. Now, divide both sides by \( (b_1 + b_2) \) to solve for \( h \):
\[
h = \frac{2A}{b_1 + b_2}
\]

Thus, the correct rearranged formula for \( h \) is:
\[
h = \frac{2A}{b_1 + b_2}
\]

So the correct response is:
\[
h = \frac{2A}{b_1 + b_2}
\]