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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

1 answer

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.