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All courses Math Foundations · MF.GM.5 52 of 60
Find and interpret surface area of prisms and cylinders.

Add the areas of all prism faces

Problem
Calculate the total surface area, in square units, of a rectangular prism with length \(3~\text{units}\), width \(4~\text{units}\), and height \(5~\text{units}\).
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Hint

Start by finding the areas of the three different face types: length × width, length × height, and width × height.

Surface area means the total area of all 6 outside faces. In a rectangular prism, each face type appears twice, so you can use 2lw + 2lh + 2wh.

Solution walkthrough

01

Use the rectangular-prism surface formula

\[SA=2lw+2lh+2\text{wh}\]

A rectangular prism has two matching faces for each pair of dimensions.

02

Source the dimensions

\[l=3;~w=4;~h=5~\text{units}\]

The prompt gives length three, width four, and height five units.

03

Substitute by face pair

\[SA=2(3\times~4)+2(3\times~5)+2(4\times~5)\]

Count two 3-by-4 faces, two 3-by-5 faces, and two 4-by-5 faces.

04

Calculate and check all six faces

\[SA=24+30+40=94~\text{square}~\text{units}\]

The three paired-face contributions total ninety-four square units.

05

Report total surface area

\[94~\text{square}~\text{units}\]

All six exterior faces together cover ninety-four square units.

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Another way

  1. List individual face areas 12,12,15,15,20,20 and add them to get 94.

!

Common mistake

Do not calculate 3×4×5; that is volume, not the sum of face areas.

Solution walkthrough video