Question

A certain hexagonal prism has a volume of 160 cubic meters. Its base has a perimeter of 30 meters and an area of 64 square meters. What is the surface area, in square meters, of the hexagonal prism?

Answer 1

Given:
hexagonal prism:
volume = 160 cubic meters
base perimeter = 30 meters
base area = 64 sq. meters

hexagon has 6 sides.
30 meters / 6 = 5 meters

Base area of hexagonal prism = (3√3)/2 * a²
Volume of hexagonal prism = (3√3)/2 * a² * h

height of the prism = volume / base area = 160 cubic meters / 64 sq. meters = 2.5 meters

Base area = 64 sq. meters * 2 faces = 128 sq. meters.
sides = 5 meters * 2.5 meters = 12.5 meters * 6 sides = 75 sq. meters

Surface area = 128 sq. meters + 75. sq. meters = 203 sq. meters