Question

find the perimeter and area of the polygon shown below.
15 ft
20 ft
8 ft
17 ft
p = 95 feet, a = 420 square feet
p = 80 feet, a = 368 square feet
p = 60 feet, a = 368 square feet
p = 80 feet, a = 360 square feet

Explanation:

Step1: Calculate the perimeter

The polygon has side - lengths 15 ft, 20 ft, 17 ft, and the remaining horizontal and vertical sides. The horizontal side parallel to the 20 - ft side can be found by considering the right - triangle part. The vertical side of the right - triangle is 15 ft and the hypotenuse is 17 ft. Using the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), if \(c = 17\) and \(a = 15\), then \(b=\sqrt{17^{2}-15^{2}}=\sqrt{(17 + 15)(17 - 15)}=\sqrt{32\times2}=\sqrt{64}=8\) ft. The perimeter \(P=15 + 20+17+(20 - 8)=80\) ft.

Step2: Calculate the area

The polygon can be split into a rectangle and a right - triangle. The rectangle has length 20 ft and width 15 ft, and the right - triangle has base 8 ft and height 15 ft. The area of the rectangle \(A_{1}=20\times15 = 300\) square feet. The area of the right - triangle \(A_{2}=\frac{1}{2}\times8\times15=60\) square feet. The total area \(A=A_{1}+A_{2}=300 + 60=360\) square feet.

Answer:

D. \(P = 80\) feet, \(A = 360\) square feet