Question

a rectangular paperboard measuring 26 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 \(A = l\times w\), where \(l = 26\) in and \(w = 18\) in.
\(A_{rectangle}=26\times18 = 468\) in²

Step2: Calculate the area of the semicircle

The diameter of the semicircle is \(d = 18\) in, so the radius \(r=\frac{d}{2}=\frac{18}{2}=9\) in.
The formula for the area of a semicircle is \(A=\frac{1}{2}\pi r^{2}\). Using \(\pi = 3.14\) and \(r = 9\) in.
\(A_{semicircle}=\frac{1}{2}\times3.14\times9^{2}=\frac{1}{2}\times3.14\times81 = 1.57\times81=127.17\) in²

Step3: Calculate the remaining area

Subtract the area of the semicircle from the area of the rectangle.
\(A_{remaining}=A_{rectangle}-A_{semicircle}\)
\(A_{remaining}=468 - 127.17=340.83\) in²

Answer:

\(340.83\) in²