Question

A rectangular paperboard measuring long and wide has a semicircle cut out of it, as shown below

Answer 1

Given:

• Length of rectangular paperboard, L = 33 in

,

• Width of rectangular paperboard, W = 23 in

,

• Diameter of the semi-circle, d = 23 in

Let's solve for the perimeter of the paperboard remaining after the semi-circle is removed.

To find the perimeter remaining, we have:

Perimeter remaining = Perimeter of rectangle - Perimeter of semi-circle.

To find the perimeter of the rectangle, apply the formula:

P = 2(L + W)

Thus, we have:

P = 2(33 + 23)

P = 2(56)

P = 112 in

The perimeter of the rectangle before the semi-circle is removed is 112 in.

• To find the Perimeter of the semi-circle, we have:

`\begin{gathered} C=(\pi d)/(2)+d \\ \\ C=(3.14*23)/(2)+23 \\ \\ C=36.11\text{ +23 =59.11 in} \end{gathered}`

The Perimeter of the semi-circle is 59.11 in

Now, to find the perimeter remaining, we have:

Perimeter remaining = Permeter of rectangle - Perimeter of semi-circle

Perimeter remaining = 112 - 59.11

Perimeter remaining = 52.89 in

Therefore, the perimeter that remains is 52.89 in.

ANSWER:

52.89 in