Question

A candy bar box is in the shape of a triangular prism. The volume of the box is 2,400 cubic centimeters. A triangular prism is shown with base of triangle labeled 16 cm, sides of triangles labeled 17 cm, and length of the box equal to 20 cm. Part A: What is the height of the base? Show your work. Part B: What is the approximate amount of cardboard used to make the candy box? Explain how you got your answer.

m a k e y o u r a n s w e r s i m p l e

Answer 1

Part A: height = 15 cm

Part B: 1240 cm²

Explanation:

Part A

Volume of a triangular prism = 1/2 x triangle base x triangle height x length

⇒ 2400 = 1/2 x 16 x h x 20

⇒ 2400 = 160h

⇒ h = 2400 ÷ 160

⇒ h = 15 cm

Part B

We need to work out the surface area of the prism.

The prism comprises 2 congruent triangles, 2 congruent "side" rectangles and 1 base rectangle.

Area of a triangle = 1/2 x base x height

⇒ area of triangle = 1/2 x 16 x 15 = 120 cm²

Area of a rectangle = width x length

⇒ area of "side" rectangle = 17 x 20 = 340 cm²

⇒ area of "base" rectangle = 16 x 20 = 320 cm²

Total surface area = (2 x 120) + (2 x 340) + 320 = 1240 cm²