math help=areas and volume of pentagonal prism?

Question

lateral, surface area, and volume of a pentagonal prism that has a radius of 8 inches and is 10 inches in height.
help me? :)

Answer 1

r=8
center angle=360/5=72
base area=1/2*8*8*sin72
=160sin72

from cos teorem
a=sqrt(128-128cos72)

V=base area*height
=160sin72

Lateral area=5*h*a
=5*10*sqrt(128-128cos72)
=50*sqrt(128-128cos72)

use your calculator

Answer 2

Lateral Surface area = Perimeter of the base * height

= (5*8) 10
= 400 inches

Total surface area = surface area + 2 * base area
= 400 + 2 * area of the pentagonal base

Volume of the prism = Area of the base * height
= Area of the pentagonal base * 10 Inches square