Question 4 (Essay Worth 10 points) (05.05 HC)

A candy bar box is in the shape of a triangular prism. The volume of the box is 3,240 cubic centimeters.

Part A: What is the height of the base? Show your work. (5 points)

Part B: What is the approximate amount of cardboard used to make the candy box? Explain how you got your answer. (5 points)

Step-by-step explanation:

Find the height using Pythagoras.

height = sqrt(hypotenuse^2 - (1/2*base^2) )

height = sqrt(15^2 - (1/2 * 24)^2  )

height = sqrt(225 - 12^2)

height = sqrt(225 - 144)

height = sqrt(81)

height = 9

Two sides

Area one side = L*W

Area one side = 30 * 15

Area one side = 450 cm^2

Area of both sides =                                          900 cm^2

Triangular base

Area one triangle = 1/2 * base * height

Area one  triangle = 1/2 * 24 * 9

Area one triangle = 12 * 9

Area one triangle = 108

Area both triangles =                                         216 cm^2

Flat bottom

Area = L * W

Area = 30 * 24

Area =                                                                720 cm^2

Total amount needed                                       1836 cm^2