Question

find the area to the nearest square foot of the shaded region below, consisting of a square with a circle cut out of it. use 3.14 as an approximation for π.

54 square feet
79 square feet
214 square feet
22 square feet

Explanation:

Step1: Calculate the area of the square

The side length of the square is equal to the diameter of the circle, which is \(10\) ft. The area of a square \(A_{square}=s^{2}\), where \(s = 10\) ft. So \(A_{square}=10\times10=100\) square feet.

Step2: Calculate the area of the circle

The formula for the area of a circle is \(A_{circle}=\pi r^{2}\). Given that the diameter \(d = 10\) ft, the radius \(r=\frac{d}{2}=\frac{10}{2}=5\) ft. Using \(\pi = 3.14\), we have \(A_{circle}=3.14\times5^{2}=3.14\times25 = 78.5\) square feet.

Step3: Calculate the area of the shaded region

The area of the shaded region \(A=A_{square}-A_{circle}\). Substitute the values: \(A = 100 - 78.5=21.5\approx22\) square feet.

Answer:

22 square feet