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=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

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

b1=2Ah−b2
b subscript 1 baseline dequals Start Fraction 2 upper A over h End Fraction minus b subscript 2 baseline

Answer 1

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

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

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

3. Divide both sides by \( (b_1 + b_2) \):
\[
h = \frac{2A}{b_1 + b_2}
\]

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

From the provided options, this corresponds to:
**h equals Start Fraction 2 upper A over b subscript 1 baseline plus b subscript 2 baseline End Fraction**.