A right pentagonal prism has a height of 6 in. The regular pentagon has a side length of 2 in.

Question

Find the surface area of the prism.

Answer 1

Given that pentagonal prism has hieght = 6.in

The regular pentagon has side of length = 2.in

Surface area of a prism = 2( Base area ) + ( perimeter * hieght)

Base area = (1/2) (n * side * apthoem)

Apthoem = (s) / 2(tan(180)/n)

               = 2 / 2(tan(180)/5)

               = 1 / (tan(36))

               = 1 / 0.7265 = 1.3764

Base area = 1/2 ( 5* 2 * 1.3764)

                = 5 * 1.3764 = 6.882

Perimeter = 5*(side)

                = 5*(2) = 10

Perimeter * hieght = 10 * (6) = 60

Surface area = 2 ( base ) + perimeter * hieght

                      = 2 * 6.882 + 60

                      = 13.764 + 60

                      = 73.764cub.inches