Answer:
[tex]\text{ 67.03 in}[/tex]
Explanation:
Here, we want to get the perimeter of the given shape
To do this, we have to subtract the perimeter (circumference) of the semi-circle from the perimeter of the full paper
Mathematically, we can calculate the perimeter of the rectangular paper as follows:
[tex]\text{ P = 2(l + b)}[/tex]
We have the dimensions of the paperboard as 21 in by 29 in
The perimeter is thus:
[tex]\text{ P = 2(21 + 29) = 2(50) = 100 in}[/tex]
We move on to calculate the circumference of the semi-circle
Mathematically, we have that as:
[tex]C\text{ = }\frac{\pi\times d}{2}[/tex]
d represents the diameter of the semi-circle which is 21 in
Thus, we have the circumference calculated as:
[tex]C\text{ = }\frac{3.14\times21}{2}\text{ = 32.97 in}[/tex]
Finally, we subtract the circumference from the total perimeter as follows:
[tex]\text{ 100 - 32.97 = 67.03 in}[/tex]
