One of the 3-dimensional figures you will explore is a prism. In this lesson, you will focus on triangular prisms and rectangular prisms. Recall that a prism is named by its congruent, parallel bases, so a triangular prism is a prism whose bases are triangles.

The Sparklee Jewelry Store is making small boxes in the shapes of rectangular prisms. The bases of each box will be green, and the lateral faces will be purple and red.

Use the activity below the following table to complete the table. Copy the table into your notes and record your answers.

Click on the image below to access the interactive. Scroll down the page to see the Geogebra applet.

Click here forInteractive popup. Assistance may be required.directions on how to use the applet.

Check Your Answers

Length	Width	Height	Lateral Surface Area	Total Surface Area
2.5 cm	3.5 cm	2 cm	24 cm3	41.5 cm3
3.5 cm	3.5 cm	2 cm	28 cm3	52.5 cm3
4 cm	2.5 cm	2.5 cm	32.5 cm3	52.5 cm3
3 cm	3.5 cm	4.5 cm	58.5 cm3	79.5 cm3

Triangular Prisms

Sparklee Jewelry Store is also creating boxes in the shapes of right triangular prisms.

In the figure below, drag the dimensions from the prism onto the appropriate place in the formula to calculate the lateral surface area of the box.

Now that you have correctly identified the dimensions, calculate the lateral surface area of the box.

Check Your Answer

180 square centimeters

The manager of Sparklee Jewelry Store wants to calculate how much cardboard will be required to manufacture each box. If each box is created from a net, what will be the total amount of cardboard required, not counting any waste, to manufacture the box?

In the figure below, drag the dimensions from the prism onto the appropriate place in the formula to calculate the total surface area of the box.

Now that you have correctly identified the dimensions, calculate the total surface area of the box.

Check Your Answer

228 square centimeters

Practice

A pencil box is in the shape of a rectangular prism and has the dimensions shown below.

1. Calculate the total surface area of the prism. Use the grid below to record your answer. Type your answer in the boxes in front of and behind the decimal. Click inside each box to enter the numeral that belongs in the box, and then click the bubble beneath the numeral to shade the bubble that matches the numeral. Incorrect portions of your answer will be shaded gray.

2. A tent is shaped like an isosceles triangular prism.

Calculate the total amount of canvas it would take to completely cover all 5 faces of the tent.

Hint

Use the formula, SA = Ph + 2B.

Check Your Answer

SA = (52 over 5 2 5 ft + 52 over 5 2 5 ft + 6 ft)(10 ft) + 21 over 2( 1 2 )(41 over 2 1 2 ft)(6 ft) = (164 over 5 4 5 ft)(10 ft) + (41 over 2 1 2 ft)(6 ft) = 168 ft² + 27 ft² = 195 ft²