Question

a rectangular paperboard measuring 28 in long and 18 in wide has a semicircle cut out of it, as shown below.
find the area of the paperboard that remains. use the value 3.14 for π, and do not round your answer. be sure to include the correct unit in your answer.

Explanation:

Step1: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A = l\times w\). Here, \(l = 28\) in and \(w = 18\) in. So, \(A_{rectangle}=28\times18 = 504\) \(in^{2}\).

Step2: Calculate the area of the semicircle

The formula for the area of a full - circle is \(A=\pi r^{2}\), and for a semicircle \(A_{semicircle}=\frac{1}{2}\pi r^{2}\). Given the diameter \(d = 18\) in, the radius \(r=\frac{d}{2}=\frac{18}{2}=9\) in. Substitute \(\pi = 3.14\) and \(r = 9\) into the formula: \(A_{semicircle}=\frac{1}{2}\times3.14\times9^{2}=\frac{1}{2}\times3.14\times81 = 127.17\) \(in^{2}\).

Step3: Calculate the remaining area

The remaining area \(A = A_{rectangle}-A_{semicircle}\). So, \(A=504 - 127.17=376.83\) \(in^{2}\).

Answer:

\(376.83\) \(in^{2}\)