Question

find the perimeter and area of the polygon shown below.

13 ft
20 ft

p = 80 feet, a = 368 square feet

p = 60 feet, a = 368 square feet

p = 80 feet, a = 360 square feet

p = 95 feet, a = 420 square feet

Explanation:

Step1: Calculate the perimeter

The perimeter \(P\) of a polygon is the sum of all its side lengths.
For the given polygon, the side lengths are \(13\) ft, \(20\) ft, \(17\) ft, and \((20 - 8+20)\) ft.

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Step2: Calculate the area

The area \(A\) of the polygon can be found by splitting it into a rectangle and a trapezoid (or using the formula for the area of a composite - shape).
The area of the rectangle part: \(A_{1}=13\times(20 - 8)=13\times12 = 156\) square feet.
The area of the parallelogram - like part (base \(b = 20\) ft, height \(h = 13\) ft): \(A_{2}=20\times13=260\) square feet (alternatively, using the formula for the area of a trapezoid \(A=\text{height}\times(\text{average of parallel sides})\), here height \(h = 13\) ft, parallel sides \(a=(20 - 8)\) and \(b = 20\), \(A=13\times\frac{(20 - 8)+20}{2}+13\times8\), but a simpler way is to consider it as a combination of a rectangle and a parallelogram).

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Answer:

\(P = 80\) feet, \(A = 368\) square feet (the first option)