Question

a. write the formula for the area a of a trapezoid. use ( b_1 ) and ( b_2 ) for the lengths of the bases
( a=)

b. solve the formula for h.
( h=)

c. use the new formula to find the height h of the trapezoid.

the height of the trapezoid is centimeters.

Explanation:

Step1: Write the formula for the area of a trapezoid

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

Step2: Solve the formula for \(h\)

Starting with \(A=\frac{1}{2}(b_1 + b_2)h\), multiply both sides by \(2\) to get \(2A=(b_1 + b_2)h\). Then divide both sides by \((b_1 + b_2)\) to obtain \(h=\frac{2A}{b_1 + b_2}\).

Step3: Find the height \(h\) of the trapezoid

Given \(A = 72\space cm^2\), \(b_1=8\space cm\), and \(b_2 = 16\space cm\). Substitute these values into the formula \(h=\frac{2A}{b_1 + b_2}\).

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Answer:

a. \(A=\frac{1}{2}(b_1 + b_2)h\)
b. \(h=\frac{2A}{b_1 + b_2}\)
c. The height of the trapezoid is \(6\) centimeters.