finding the perimeter and area of a polygon

Question

Find the perimeter and area of the following polygon: a pentagon with a 3 ft radius.

Answer 1

The central angle of a regular pentagon measures 360/5=72°.

Two 3' radii and a side of the pentagon form an isosceles triangle, the base of which is 2×3sin36=6sin36=3.5267' approx. So the perimeter measures 5×6sin36=30sin36=17.6336' approx.

The area of the isosceles triangle=3²sin72°/2=4.2798ft² approx, making the area of the pentagon 5 times this: 21.3988ft².