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 answe

Explanation:

Step1: Calculate the area of the rectangle

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

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

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

Step3: Calculate the remaining area

The remaining area \(A = A_{rectangle}-A_{circle}\)
\(A=312 - 113.04=198.96\) \(cm^{2}\)

Answer:

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