Question

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

Answer 1

219.52 in²

Explanation

The remaining area is calculated as follows:

`A_(remaining)=A_(rectangle)-A_(semicircle)`

The area of the rectangle is calculated as follows:

`\begin{gathered} A_(rectnagle)=length* width \\ A_(rectnagle)=20*16 \\ A_(rectnagle)=320\text{ in}{}^2 \end{gathered}`

The area of the semicircle is calculated as follows:

`\begin{gathered} A_(semicircle)={(\pi(diameter)^2)/(8)} \\ A_(sem\imaginaryI c\imaginaryI rcle)={(3.14(16)^2)/(8)} \\ A_{sem\mathrm{i}c\mathrm{i}rcle}=100.48\text{ in}^2 \end{gathered}`

Finally, the area of the paperboard that remains is:

`\begin{gathered} A_(remaining)=320-100.48 \\ A_(rema\imaginaryI n\imaginaryI ng)=219.52\text{ in}^2 \end{gathered}`