Question

find the perimeter and area of the polygon shown below.

p = 56 feet, a = 308 square feet
p = 72 feet, a = 300 square feet
p = 87 feet, a = 360 square feet
p = 72 feet, a = 308 square feet

Explanation:

Step1: Calculate the perimeter

The perimeter \(P\) of the polygon is the sum of all its side lengths.
The sides are \(15\) ft, \(16\) ft, \(17\) ft, and \((16 - 8)+16=24\) ft.
\(P=15 + 16+17+(16 - 8 + 16)\)
\(P=15+16 + 17+24\)
\(P = 72\) feet.

Step2: Calculate the area

The area \(A\) of the polygon can be found by splitting it into a rectangle and a right - triangle.
The area of the rectangle is \(15\times16 = 240\) square feet.
The area of the right - triangle: base \(b = 8\) ft, height \(h=15\) ft. Using the formula \(A_{\triangle}=\frac{1}{2}bh\), we have \(A_{\triangle}=\frac{1}{2}\times8\times15=60\) square feet.
The total area \(A=240 + 60=300\) square feet.

Answer:

\(P = 72\) feet, \(A = 300\) square feet (the second option).