Question

find the perimeter and area of the polygon shown below.
15 ft
16 ft
8 ft
17 ft
p = 87 feet, a = 360 square feet
p = 56 feet, a = 308 square feet
p = 72 feet, a = 308 square feet
p = 72 feet, a = 300 square feet

Explanation:

Step1: Calculate the perimeter

The polygon has side - lengths 15 ft, 16 ft, 17 ft, and we need to find the length of the fourth side. The horizontal part of the figure shows that the missing horizontal length of the fourth - side is \(16 - 8=8\) ft. The vertical part is 15 ft. Using the Pythagorean theorem for the non - vertical and non - horizontal side is not needed as we can directly sum the side - lengths. The perimeter \(P=15 + 16+17+(8 + 15)\)

$$P=15 + 16+17+23=72$$

Step2: Calculate the area

We can split the polygon into a rectangle and a triangle. The rectangle has length 16 ft and width 15 ft, and the triangle has base \(16 - 8 = 8\) ft and height 15 ft.
The area of the rectangle \(A_{1}=16\times15 = 240\) square feet.
The area of the triangle \(A_{2}=\frac{1}{2}\times8\times15=60\) square feet.
The total area \(A = A_{1}+A_{2}=240 + 60=300\) square feet.

Answer:

P = 72 feet, A = 300 square feet