Question

In a regular pentagon, the anthem measures 6.2 mm. A) what is the length of one side? B) what is it's perimeter? C) what is the area of the regular polygon?

Answer 1

Use SOHCAHTOA

Find the central angle
360/5
72
72/2
36

You now have a right triangle where the angle is 36 and one side is 6.2

You need to find a side

Use tan because it is opposite (side/2) and you have the adjacent (6.2)

Tan36 = s(/2) / 6.2
6.2tan36 = 4.5
4.5 x 2 = 9

One side is 9 mm

9 x 5 is 45

Perimeter = 45 mm

Use perimeter x apothem / 2 to find the area

6.2 x 45 / 2

Area is 139.5 mm squared