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:
[tex]\begin{gathered} C=\frac{\pi d}{2}+d \\ \\ C=\frac{3.14*23}{2}+23 \\ \\ C=36.11\text{ +23 =59.11 in} \end{gathered}[/tex]
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
