MATH SOLVE

2 months ago

Q:
# 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.

Accepted Solution

A:

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

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