Question

A rectangular paperboard measuring 32 in long and 24 in wide has a semicircle cut out of it, as shown below.Find the area of the paperboard that remains. Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.

Answer 1

We need to subtract the area of the semicircle that was cut out of the paperboard from its original area.

The original area of the paperboard was the area of a rectangle 32in long and 24 in wide:

`32in\cdot24in=768in^(2)`

And the area of the semicircle, noticing that its radius r is 24in/2, is given by:

`(\pi r^2)/(2)=(3.14\cdot(12in)^(2))/(2)=(3.14\cdot144in^2)/(2)=226.08in^2`

Thus, the area of the paperboard that remains is:

`768in^2-226.08in^2=(768-226.08)in^(2)=541.92in^(2)`

Therefore, the answer is 541.92 in².