How to Find the Surface Area of a Rectangular Prism

Geometry · Volume and surface area

How to Find the Surface Area of a Rectangular Prism

Problem

4 \times 3 \times 5

Answer

SA = 94

Surface area is the total area of the outside of a solid. For a rectangular prism, find three face areas, add them, then double the sum.

Step-by-step solution

Write the surface area formula.
$SA = 2(lw + lh + wh)$
Why: A box has three pairs of matching faces.
Work out the three face areas.
$lw = 12,\quad lh = 20,\quad wh = 15$
Why: Each product is the area of one face.
Add the three face areas.
$12 + 20 + 15 = 47$
Why: The sum covers one face from each pair.
Double the sum.
$SA = 2 \times 47 = 94$
Why: Each face has an opposite face of the same size.

Common mistakes

Forgetting to double the sum. There are six faces, not three.
Using the volume formula. Volume has three lengths; surface area has two.
Mixing the face pairs, such as using 4 x 3 twice.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

$2 \times 3 \times 4$

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$SA = 52$
$5 \times 5 \times 2$

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$SA = 90$
$3 \times 4 \times 6$

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$SA = 108$
$2 \times 2 \times 2$

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$SA = 24$
$1 \times 3 \times 5$

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$SA = 46$