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

Answer

219.52 in²

Step-by-step explanation

The remaining area is calculated as follows:

$A_{remaining}=A_{rectangle}-A_{semicircle}$

The area of the rectangle is calculated as follows:

$\begin{gathered} A_{rectnagle}=length\times width \\ A_{rectnagle}=20\times16 \\ A_{rectnagle}=320\text{ in}{}^2 \end{gathered}$

The area of the semicircle is calculated as follows:

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

Finally, the area of the paperboard that remains is:

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