Question

find the perimeter and area of the polygon shown below.

p = 80 feet, a = 368 square feet

p = 95 feet, a = 420 square feet

p = 80 feet, a = 360 square feet

p = 60 feet, a = 368 square feet

Explanation:

Step1: Calculate the perimeter

The perimeter \(P\) of the polygon is the sum of all its side lengths.
\(P=15 + 20+17+(20 - 8)+15\)
\(P=15+20 + 17+12+15\)
\(P = 80\) feet.

Step2: Calculate the area

The area \(A\) of the polygon is the sum of the area of the rectangle and the area of the triangle.
The area of the rectangle \(A_{1}=15\times(20 - 8)=15\times12 = 180\) square feet.
The base of the triangle \(b = 8\) feet and the height \(h=15\) feet. The area of the triangle \(A_{2}=\frac{1}{2}\times8\times15=60\) square feet.
\(A=180+(15\times20)=180 + 180=360\) square feet.

Answer:

\(P = 80\) feet, \(A = 360\) square feet (the third option).