Question

a rectangular paperboard measuring 20 in long and 13 in wide has a semicircle cut out of it, as shown below. what is the perimeter of the paperboard that remains after the semicircle is removed? (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 perimeter of the rectangle without the bottom side

The formula for the perimeter of a rectangle is \(P = 2(l + w)\). Here, we exclude the bottom side. So the length of the two vertical sides is \(2\times20 = 40\) inches, and the length of the top side is \(13\) inches.

Step2: Calculate the length of the semicircle arc

The formula for the circumference of a full - circle is \(C=2\pi r\). For a semicircle, \(C_{semicircle}=\pi r\). Given the diameter \(d = 13\) inches (so the radius \(r=\frac{13}{2}\) inches), and using \(\pi = 3.14\), we have \(C_{semicircle}=3.14\times\frac{13}{2}=3.14\times6.5 = 20.41\) inches.

Step3: Sum up the lengths

The total perimeter \(P=40 + 13+20.41\) inches.

Answer:

\(73.41\) in