Question

A candy bar box is in the shape of a triangular prism. The volume of the box is 1,200 cubic centimeters. A triangular prism is shown with base of triangle labeled 10 cm, sides of the triangles labeled 13 cm, and length of the box equal to 20 cm. 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).

Answer 1

The height of the base is 12cm.

The approximate amount of cardboard used to make the candy box is  720 cm².

Given

A candy bar box is in the shape of a triangular prism.

The volume of the box is 1,200 cubic centimeters.

A triangular prism is shown with a base of the triangle labeled 10 cm, sides of the triangles labeled 13 cm, and length of the box equal to 20 cm.

The volume of the prism;

The volume of a triangular prism is given by the formula;

$\rm Volume=\dfrac{1}{2} \times length \times width \times height$

Part A: What is the height of the base?

The height of the base is given by;

$\rm Volume=\dfrac{1}{2} \times length \times width \times height\\\\1200=\dfrac{1}{2}\times 20 \times 10 \times Height\\\\Height =\dfrac{1200\times 2}{20 \times 10}\\\\Height =\dfrac{2400}{200}\\\\Height = 12 \ cm$

The height of the base is 12cm.

Part B: What is the approximate amount of cardboard used to make the candy box?

The approximate amount of cardboard used to make the candy box is given by;

$\rm Area = 2 \times length \times width+ length \times width \\\\Area = 2\times 20 \times 10+ 20\times 10\\\\Area = 520+200 \\\\Area = 720$

The approximate amount of cardboard used to make the candy box is  720 cm².

To know more about triangular prism click the link given below.

brainly.com/question/17056191