Question

find the area of the shaded region. 16 ft 16 ft

Explanation:

Step1: Calculate the area of the square

The area formula for a square is \(A = s^2\), where \(s\) is the side - length. Given \(s = 16\) ft, so \(A_{square}=16\times16 = 256\) \(ft^{2}\).

Step2: Calculate the area of the circle

The diameter of the circle \(d = 16\) ft, so the radius \(r=\frac{d}{2}=\frac{16}{2}=8\) ft. The area formula for a circle is \(A=\pi r^{2}\), taking \(\pi = 3.14\), then \(A_{circle}=3.14\times8^{2}=3.14\times64 = 200.96\) \(ft^{2}\).

Step3: Calculate the area of the triangle

The base of the triangle \(b = 16\) ft and the height \(h = 8\) ft. The area formula for a triangle is \(A=\frac{1}{2}bh\), so \(A_{triangle}=\frac{1}{2}\times16\times8=64\) \(ft^{2}\).

Step4: Calculate the area of the shaded region

The area of the shaded region \(A = A_{square}-A_{circle}+A_{triangle}\).
Substitute the values: \(A = 256-200.96 + 64\).
First, \(256-200.96=55.04\), then \(55.04 + 64=119.04\) \(ft^{2}\).

Answer:

\(119.04\) \(ft^{2}\)