Question

geometry what is the length of the missing base of the trapezoid? 3 in area - 21 in. 8 in. in.

Explanation:

Step1: Recall the area formula of trapezoid

The area formula of a trapezoid is \(A=\frac{(a + b)h}{2}\), where \(A\) is the area, \(a\) and \(b\) are the bases, and \(h\) is the height. We know \(A = 21\space in^{2}\), \(h=3\space in\), \(a = 8\space in\), and we need to find \(b\).

Step2: Substitute the known values into the formula

Substitute into \(A=\frac{(a + b)h}{2}\), we get \(21=\frac{(8 + b)\times3}{2}\).
First, multiply both sides of the equation by \(2\): \(21\times2=(8 + b)\times3\), so \(42=(8 + b)\times3\).
Then divide both sides by \(3\): \(\frac{42}{3}=8 + b\), \(14=8 + b\).

Step3: Solve for \(b\)

Subtract \(8\) from both sides: \(b=14 - 8\).

Answer:

\(6\)