Question

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

b1=2Ah−b2
b subscript 1 baseline dequals Start Fraction 2 upper A over h End Fraction minus b subscript 2 baseline
h=b1+b22A
h equals Start Fraction b subscript 1 baseline plus b subscript 2 baseline over 2 upper A End Fraction
h=2Ab1+b2
h equals Start Fraction 2 upper A over b subscript 1 baseline plus b subscript 2 baseline 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

Answer 1

To rearrange the area formula for a trapezoid, which is given by

\[ A = \frac{1}{2}h(b_1 + b_2) \]

for \( h \), follow these steps:

1. Multiply both sides by \( 2 \) to eliminate the fraction:

\[ 2A = h(b_1 + b_2) \]

2. Now, divide both sides by \( (b_1 + b_2) \) to isolate \( h \):

\[ h = \frac{2A}{b_1 + b_2} \]

Thus, the correct rearranged formula for \( h \) in terms of \( A \), \( b_1 \), and \( b_2 \) is:

\[ h = \frac{2A}{b_1 + b_2} \]

So the correct response is:

**h = \(\frac{2A}{b_1 + b_2}\)**.