Question

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

Responses

h=b1+b22Ah=b1+b22A

h equals Start Fraction b subscript 1 baseline plus b subscript 2 baseline over 2 upper A End Fraction

b1=2Ah−b2b1=2Ah−b2

b subscript 1 baseline dequals Start Fraction 2 upper A over h End Fraction minus b subscript 2 baseline

h=12A(b1+b2)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

Answer 1

The formula for the area of a trapezoid is \( A = \frac{1}{2}h(b_1 + b_2) \).

To rearrange this for \( h \):

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

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

So the correct response that expresses \( h \) in terms of \( A \), \( b_1 \), and \( b_2 \) is:
\[
h = \frac{2A}{b_1 + b_2}
\]