Question

A rectangular paperboard measuring 33 in long and 21 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 it, and do not round your answer. Be sure to include the correct unit in your answer.)

Answer 1

Explanation

The question wants us to obtain the perimeter of the paperboard that remains after the semicircle has been removed

To do so, we will follow the steps below:

Step1: Find the Perimeter of the rectangle

The perimeter of a rectangle is simply the sum of all its sides

So in our case, we will have to sum sides A as given below

$Perimeter\text{ of rectangle= 21 +33+33= 87 inches}$

Step 2: Find the perimeter of the semi-circle

The perimeter of a semi-circle is given by:

$\begin{gathered} \frac{\pi D}{2} \\ where \\ \pi=3.14 \\ D=diameter\text{ of the semicircle =21 inches} \end{gathered}$

Simplifying

$Perimeter\text{ of semicircle=}\frac{3.14\times21}{2}=32.97\text{ inches}$

Step 3: Find the sum of the perimeters of the rectangle and semicircle

Therefore, the perimeter of the paperboard that remains after the semicircle is removed will be

$\begin{gathered} perimeter\text{ }of\text{ }the\text{ }rectangle+\text{ perimeters of the semicircle =87inches + 32.97 inches} \\ perimeter\text{ }of\text{ }the\text{ }rectangle-\text{ perimeters of the semicircle =119.97 inches} \end{gathered}$

Hence, the perimeter of the paperboard that remains after the semicircle is removed will be 119.97 in