Question

find the area of the shaded region below. (assume ( a = 14 ) in. assume that given measurements are exact, and round approximate answers to the nearest tenth of a square unit.) (square mathrm{in}^{2})

Explanation:

Step1: Find the radius of the circle

The diameter \(a = 14\) in. The radius \(r=\frac{a}{2}\).
So, \(r=\frac{14}{2}=7\) in.

Step2: Use the formula for the area of a circle

The formula for the area of a circle is \(A=\pi r^{2}\).
Substitute \(r = 7\) into the formula: \(A=\pi\times(7)^{2}\).
Since \(\pi\approx3.14\), then \(A = 3.14\times49\).
\(A=153.86\approx153.9\) in².

Answer:

\(153.9\) in²