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?

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