Question

A rectangular paperboard measuring 23 in long and 18 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 n, and do not round your answer. Be sure to include the correct unit in your answer.)

Answer 1

We shall begi by determining the size of the arc that was cut out of the rectangular paperboard.

`\begin{gathered} \text{Circumerence o a circle is given as;} \\ \text{Cir}=2\pi r \\ \text{Where, }\pi=3.14,r=9\text{ in} \\ (1)/(2)\text{Cir}=(1)/(2)(2*3.14*9) \\ (1)/(2)\text{Cir}=3.14*9 \\ (1)/(2)\text{Cir}=28.26 \end{gathered}`

Observe that the new shape now consists of two lengths measuring 23 inches each, and one width measuring 18 inches, and the half circumerence measuring 28.26 inches.

The perimeter therefore is the addition of all sides and that is;

Perimeter = 23 + 23 + 18 + 28.26

Perimeter = 92.26 inches