Question

A rectangular paperboard measuring 25 in long and 16 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 IT, and do not round your answer. Be sure to include the correct unit in your answer

Answer 1

To answer this question we will use the following diagram as a reference:

The semicircle's radius is 8in.

Notice that the area of the paperboard that remains is the area of the rectangular paper board minus the area of the semicircle.

The semicircle's area is:

`A_s=(\pi(8in)^2)/(2)=(64\pi)/(2)in^2=32\pi in^2\approx100.48in^2.`

The rectangle's area is:

`A_r=16in*25in=400in^2.`

Then the area of the paperboard that remains:

`\begin{gathered} A=400in^2-100.48in^2 \\ =299.52in^2. \end{gathered}`

Answer:

`299.52in^2.`