Question

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

Explanation:

Step1: Calculate the perimeter

Add up the side - lengths of the polygon. The side - lengths are 15 ft, 16 ft, 17 ft, 8 ft, and the vertical and horizontal parts that can be deduced from the figure. The perimeter $P=15 + 16+17 + 8+(16 - 8)+(15)=72$ feet.

Step2: Calculate the area

Split the polygon into a rectangle and a right - triangle. The rectangle has dimensions 15 ft by 16 ft and the triangle has base 8 ft and height 17 ft. The area of the rectangle $A_{rect}=15\times16 = 240$ square feet, and the area of the triangle $A_{tri}=\frac{1}{2}\times8\times17 = 68$ square feet. So the total area $A = 240+68=308$ square feet.

Answer:

$P = 72$ feet, $A = 308$ square feet