A shipping tube is shaped like a triangular prism. The bases are equilateral triangles with edges of 6 inches and a height of 5.2 inches. The tube is 14 inches long. Find the lateral surface area of the shipping tube.

The lateral surface area of the prism can be calculated by taking the sum of the area of the three lateral rectangle faces around.

3 rectangle faces - length - 14 inches

width is the hypotenuse of the triangle at the base.

using Pythagoras theorem,

if H - hypotenuse

A - height of the triangle at the base (5.2 inches)

B - half the length of the side of the equilateral triangle (6/2 = 3 inches)

H² = A² + B²

H² = 5.2² + 3²

= 27.04 + 9

= 36.04

H = 6.00 inches

hypotenuse is the width

area of rectangle = 14 inches x 6 inches = 84 inch²

there are three rectangle faces = 84 x 3 = 252 inch²