Question

A rectangular paperboard measuring 25 in long and 20 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 find the remaining area after the semicircle is cut out, you need to calculate the area of the rectangle and subtract the area of the semicircle.

1. Area of the rectangle: \(25 \, \text{in} \times 20 \, \text{in} = 500 \, \text{in}^2\)

2. Radius of the semicircle: \(20 \, \text{in} / 2 = 10 \, \text{in}\)

3. Area of the semicircle: \(\frac{1}{2} \times 3.14 \times (10 \, \text{in})^2 \approx 157 \, \text{in}^2\)

Now, subtract the area of the semicircle from the area of the rectangle:

\[500 \, \text{in}^2 - 157 \, \text{in}^2 = 343 \, \text{in}^2\]

Therefore, the area of the paperboard that remains is \(343 \, \text{in}^2\).