Question

a rectangular piece of paper with length 26 cm and width 12 cm has two semicircles cut out of it, as shown below.
find the area of the paper 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.

Explanation:

Step1: Calculate the area of the rectangle

The area formula for a rectangle is \(A = length\times width\). Given \(length = 26\space cm\) and \(width=12\space cm\), so \(A_{rectangle}=26\times12 = 312\space cm^{2}\).

Step2: Calculate the area of the two - semicircles (which is equivalent to the area of one full circle)

The diameter of the circle \(d = 12\space cm\), so the radius \(r=\frac{d}{2}=\frac{12}{2}=6\space cm\). The area formula for a circle is \(A=\pi r^{2}\). Using \(\pi = 3.14\), we have \(A_{circle}=3.14\times6^{2}=3.14\times36 = 113.04\space cm^{2}\).

Step3: Calculate the remaining area of the paper

The remaining area \(A = A_{rectangle}-A_{circle}\). Substitute the values: \(A=312 - 113.04=198.96\space cm^{2}\).

Answer:

\(198.96\space cm^{2}\)