Question

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

Answer 1

The total perimeter of the paperboard after the semicircle is removed will be:

$\text{ Perimeter = Length + Length + Width + Arc length \lparen Semi-circle\rparen}$

Let's first determine the arc length of the semicircle,

$\text{ Arc length = }\frac{\text{ Circumference }}{2}\text{ = }\frac{\pi D}{2}$

Where,

D = diameter

We get,

$\text{ Arc length = }\frac{\pi D}{2}\text{ = }\frac{(3.14)(17)}{2}\text{ = }\frac{53.38}{2}\text{ = 26.69 in.}$

Let's now determine the total perimeter:

$\text{ Perimeter = 21 + 21 + 17 + 26.69 = 85.69 in.}$

Therefore, the perimeter is 85.69 in.