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Surface Area Help

1Finding the Surface Area

2Making the Formula Shorter

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**Reviewed by**Grace Imson, MA

Last Updated: November 14, 2023Fact Checked

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A rectangular prism is a name for a 6-sided 3-dimensional figure that is very familiar to everybody—a box.^{[1]} Think of a brick, or a shoebox, and you know exactly what a rectangular prism is. The surface area is the amount of space on the outside of the object. "How much paper do I need to wrap this shoebox" sounds a lot less complicated, but it's exactly the same math problem.

### Surface Area Help

Surface Area of a Rectangular Prism Using Dimensions Cheat Sheet

Surface Area of a Rectangular Prism Using Area Cheat Sheet

Surface Area of a Rectangular Prism Calculator

Part 1

Part 1 of 2:

### Finding the Surface Area

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1

**Label the length, width, and height of your rectangular prism.**Each rectangular prism has a length, a width, and a height. Draw a picture of the prism, and write the symbols**l**,**w**, and**h**next to three different edges of the shape.^{[2]}- If you're not sure which sides to label, pick any corner. Label the three lines that meet at that corner.
- For example: A box has a base that measures 3 inches by 4 inches, and it stands 5 inches tall. The long side of the base is 4 inches, so
**l**= 4,**w**= 3, and**h**= 5.

2

**Look at the six faces of the prism.**To cover the whole surface area, you'd need to paint six different "faces." Think about each one — or find a box of cereal and look at them directly:^{[3]}- There are a top and bottom face. Both are the same size.
^{[4]} - There are a front and a back face. Both are the same size.
- There are a left and right face. Both are the same size.
- If you have trouble picturing this, cut a box apart along the edges and lay it out.
^{[5]}

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- There are a top and bottom face. Both are the same size.
3

**Find the area of the bottom face.**To start out, let's find the surface area of just one face: the bottom. This is a rectangle, just like every face. One edge of the rectangle is labeled length and the other is labeled width. To find the area of the rectangle, just multiply the two edges together.^{[6]}Area (bottom edge) = length times width =**lw**.- Going back to our example, the area of the bottom face is 4 inches x 3 inches = 12 square inches.

4

**Find the area of the top face.**Wait a second — we already noticed that the top and bottom faces are the same size. This must also have an area of**lw**^{[7]}.See AlsoSurface Area of a Prism – Explanation & ExamplesSurface Area of a Rectangular Prism CalculatorSurface Area of Prism- Formula, Definition, Solved ExamplesSurface Area of a Prism - Math Steps, Examples & Questions- In our example, the top area is also 12 square inches.

5

**Find the area of the front and back faces.**Go back to your diagram and look at the front face: the one with one edge labeled width and one labeled height. The area of the front face = width times height =**wh**. The area of the back is also**wh**.- In our example, w = 3 inches and h = 5 inches, so the area of the front is 3 inches x 5 inches =15 square inches. The area of the back face is also 15 square inches.

6

**Find the area of the left and right faces.**We've just got two faces left, each the same size. One edge is the length of the prism, and one edge is the height of the prism. The area of the left face is**lh**and the area of the right face is also**lh**.- In our example, l = 4 inches and h = 5 inches, so the area of the left face = 4 inches x 5 inches = 20 square inches. The area of the right face is also 20 square inches.

7

**Add the six areas together.**Now you've found the area of each of the six faces. Add them all together to get the area of the whole shape:**lw + lw + wh + wh + lh + lh**. You can use this formula for any rectangular prism, and you will always get the surface area.^{[8]}- To finish our example, just add up all the blue numbers above: 12 + 12 + 15 + 15 + 20 + 20 = 94 square inches.

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Part 2

Part 2 of 2:

### Making the Formula Shorter

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1

**Simplify the formula.**You now know enough to find the surface area of any rectangular prism. You can do it faster if you've learned some basic algebra. Start with our equation above: Area of a rectangular prism = lw + lw + wh + wh + lh + lh. If we combine all the terms that are the same, we get:^{[9]}- Area of a rectangular prism =
**2lw + 2wh + 2lh**

- Area of a rectangular prism =
2

**Factor out the two.**If you know how to factor in algebra, you can make it even shorter:^{[10]}- Area of a Rectangular Prism = 2lw + 2wh + 2lh =
**2(lw + wh + lh)**.

- Area of a Rectangular Prism = 2lw + 2wh + 2lh =
3

**Test it on an example.**^{[11]}Let's go back to our example box, with length 4, width 3, and height 5. Plug these numbers into the formula:- Area = 2(lw + wh + lh) = 2 x (lw + wh + lh) = 2 x (4x3 + 3x5 + 4x5) = 2 x (12 + 15 + 20) = 2 x (47) = 94 square inches. That's the same answer we got before. Once you've practiced doing these equations, this is a much faster way to find the surface area.

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## Community Q&A

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Question

How do I find the surface area of one with no length or is represented by x?

Donagan

Top Answerer

Multiply x by the width and then by the height.

**Thanks! We're glad this was helpful.****Thank you for your feedback.**

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Not Helpful 54Helpful 67

Question

How do I find the edge lengths for a rectangular prism with a surface area of 92 m?

Donagan

Top Answerer

You can't find them without having additional information.

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Question

How do I find the total surface area of a triangular prism?

Community Answer

Start off with the formula for the area of a triangle: 1/2bh = a (One half of base times height equals area.) Also, you'll need to know how to find the area of a rectangle, lw = a (length times width equals area.) Make a net of the prism. If the length and width of the prism are say, l = 4 and w = 6, the bottom rectangle in the center should be 4 x 6 (area = 24 sq. units.). Next, do the other two rectangles (Cheat: They're always the same area as the base!) Now, find the area of the triangle. Say the height = 4. We know w = 6, so we multiply 4 x 6. Now we multiply that by 1/2 (divide by 2). Do the same for the other one, then add them up.

**Thanks! We're glad this was helpful.****Thank you for your feedback.**

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## Tips

Areas always use "square units," like square inches or square centimeters.

^{[12]}A square inch is just what it sounds like: a square that's one inch wide and one inch long. If a prism has a surface area of 50 square inches, that means it takes 50 of those squares to cover every surface on the prism.Thanks

Helpful0Not Helpful0

If you don't know which way up the prism is, you can call any side the height. The length is usually the longest side, but even that's not really important. As long as you stick with the same names for the whole problem, you'll be fine.

^{[13]}Thanks

Helpful1Not Helpful0

Some teachers use "breadth" or "depth" instead of one of these names. That's fine, as long as you label each side clearly.

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## You Might Also Like

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## References

- ↑ https://www.mathsisfun.com/definitions/rectangular-prism.html
- ↑ https://flexbooks.ck12.org/cbook/ck-12-interactive-middle-school-math-7-for-ccss/section/6.5/related/lesson/surface-area-of-rectangular-prisms-msm7/
- ↑ https://www.cuemath.com/geometry/rectangular-prism/
- ↑ http://www.math.com/tables/geometry/surfareas.htm
- ↑ http://education.seattlepi.com/surface-area-rectangular-prism-fifth-graders-5826.html
- ↑ https://www.cuemath.com/measurement/surface-area-of-rectangular-prism/
- ↑ https://www.cuemath.com/measurement/surface-area-of-rectangular-prism/
- ↑ https://www.cuemath.com/measurement/surface-area-of-rectangular-prism/
- ↑ https://flexbooks.ck12.org/cbook/ck-12-interactive-middle-school-math-7-for-ccss/section/6.5/related/lesson/surface-area-of-rectangular-prisms-msm7/

More References (4)

- ↑ https://www.calculatorsoup.com/calculators/geometry-solids/rectangularprism.php
- ↑ https://flexbooks.ck12.org/cbook/ck-12-interactive-middle-school-math-7-for-ccss/section/6.5/related/lesson/surface-area-of-rectangular-prisms-msm7/
- ↑ https://www.khanacademy.org/math/pre-algebra/measurement/area-basics/v/introduction-to-area-and-unit-squares
- ↑ http://thinkmath.edc.org/resource/measurement-length-width-height-depth

## About This Article

Reviewed by:

Grace Imson, MA

Math Teacher

This article was reviewed by Grace Imson, MA. Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. This article has been viewed 1,328,887 times.

194 votes - 70%

Co-authors: 85

Updated: November 14, 2023

Views:1,328,887

Categories: Calculating Volume and Area

Article SummaryX

To find the surface area of a rectangular prism, measure the length, width, and height of the prism. Find the area of the top and bottom faces by multiplying the length and width of the prism. Then, calculate the area of the left and right faces by multiplying the width and height. Finally, find the area of the front and back faces by multiplying the length and height of the prism. To find the surface area, simply add all 6 of these areas together and write your result in square units. If you want to learn how to simplify your formulas to make them easier to remember, keep reading the article!

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