Question

=Perimeter imciding rectangles and circlesAuta paperboard measuring 29 in long and 21 in wide has a semicede cut out of it, as shown below. What is the perimeter of the papertoard etremains after the semicirde is removed? (Use the value 3.14 fore, and do not round your answer. Be sure to include the comment in your answer)

Answer 1

`\text{ 67.03 in}`

Step-by-step 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:

`\text{ P = 2(l + b)}`

We have the dimensions of the paperboard as 21 in by 29 in

The perimeter is thus:

`\text{ P = 2(21 + 29) = 2(50) = 100 in}`

We move on to calculate the circumference of the semi-circle

Mathematically, we have that as:

`C\text{ = }(\pi* d)/(2)`

d represents the diameter of the semi-circle which is 21 in

Thus, we have the circumference calculated as:

`C\text{ = }(3.14*21)/(2)\text{ = 32.97 in}`

Finally, we subtract the circumference from the total perimeter as follows:

`\text{ 100 - 32.97 = 67.03 in}`