Question

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

Explanation:

Step1: Calculate the perimeter

Add the lengths of all sides. The sides are 15 ft, 20 ft, 17 ft, and the remaining horizontal and vertical parts. The horizontal part is 20 - 8=12 ft and the vertical part is 15 ft. So $P=15 + 20+17+(20 - 8)+15=80$ ft.

Step2: Calculate the area

Split the polygon into a rectangle and a right - triangle. The rectangle has dimensions 15 ft by 20 ft and the triangle has base 8 ft and height 15 ft. The area of the rectangle $A_{rect}=15\times20 = 300$ square feet, and the area of the triangle $A_{tri}=\frac{1}{2}\times8\times15=60$ square feet. So $A = 300+60=360$ square feet.

Answer:

$P = 80$ feet, $A = 360$ square feet