How to Find the Surface Area of a Rectangular Prism: 10 Steps (2024)

  • Categories
  • Education and Communications
  • Studying
  • Mathematics
  • Geometry
  • Calculating Volume and Area

Download Article

Explore this Article

parts

Surface Area Help

1Finding the Surface Area

2Making the Formula Shorter

Other Sections

Tips and Warnings

Related Articles

References

Article Summary

Reviewed byGrace Imson, MA

Last Updated: November 14, 2023Fact Checked

Download Article

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

Download Article

  1. 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. 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]

    Advertisem*nt

  3. 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. 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].

    • In our example, the top area is also 12 square inches.
  5. 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. 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. 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.
  8. Advertisem*nt

Part 2

Part 2 of 2:

Making the Formula Shorter

Download Article

  1. 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
  2. 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).
  3. 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.
  4. Advertisem*nt

Community Q&A

Search

Add New Question

  • Question

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

    How to Find the Surface Area of a Rectangular Prism: 10 Steps (18)

    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.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission.Support wikiHow

    YesNo

    Not Helpful 54Helpful 67

  • Question

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

    How to Find the Surface Area of a Rectangular Prism: 10 Steps (19)

    Donagan

    Top Answerer

    You can't find them without having additional information.

    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission.Support wikiHow

    Not Helpful 46Helpful 53

  • Question

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

    How to Find the Surface Area of a Rectangular Prism: 10 Steps (20)

    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.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission.Support wikiHow

    YesNo

    Not Helpful 42Helpful 48

See more answers

Ask a Question

200 characters left

Include your email address to get a message when this question is answered.

Submit

      Advertisem*nt

      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.

        Thanks

        Helpful0Not Helpful0

      Submit a Tip

      All tip submissions are carefully reviewed before being published

      Submit

      Thanks for submitting a tip for review!

      How to Find the Surface Area of a Rectangular Prism: 10 Steps (21)

      Advertisem*nt

      You Might Also Like

      How toCalculate Series and Parallel ResistanceHow toCalculate the Geometric Mean
      How toChange a Common Fraction Into a DecimalHow toFind the Area and Perimeter of a RectangleHow toCalculate Square MetersHow toCalculate the Area of a CircleHow toCalculate the Area of a TriangleHow toCalculate the Area of a TrapezoidHow toCalculate the Area of a RhombusHow toCalculate the Area of a PolygonHow toFind the Area of a Regular PentagonHow toCalculate the Area of an EllipseHow toFind the Surface Area of a Box

      Advertisem*nt

      More References (4)

      About This Article

      How to Find the Surface Area of a Rectangular Prism: 10 Steps (36)

      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!

      Did this summary help you?

      In other languages

      Spanish

      Russian

      French

      Indonesian

      Chinese

      Thai

      Hindi

      Arabic

      Korean

      • Print
      • Send fan mail to authors

      Thanks to all authors for creating a page that has been read 1,328,887 times.

      Reader Success Stories

      • How to Find the Surface Area of a Rectangular Prism: 10 Steps (37)

        Wadood Abdul

        Sep 28, 2017

        "This article and other articles related to area calculation of triangles and quadrilateral of different kinds were..." more

      More reader storiesHide reader stories

      Did this article help you?

      Advertisem*nt

      How to Find the Surface Area of a Rectangular Prism: 10 Steps (2024)

      FAQs

      What is the formula for the area of the rectangular surface of a prism? ›

      Surface Area of a rectangular prism = 2 (lh +wh + lw ) Square units.

      How to find the surface area of a rectangular prism worksheet? ›

      Surface Area of a Rectangular Prism Worksheets

      It is a solid shape with 6 rectangular faces. The length l, width w, and height h are expressed in whole numbers. Apply the formula SA = 2(lw + lh+ wh), find the surface area, and represent the answer in square units.

      How to solve surface area? ›

      Surface area is total area on the surface of a three-dimensional shape. To find the surface area of a cuboid which has 6 rectangular faces, add the areas of all 6 faces. Or, you can label the length (l), width (w), and height (h) of the cuboid and use the formula: surface area (SA)=2lw+2lh+2hw.

      What is the formula for the surface area of a prism? ›

      The surface area of a prism is given as S = (2 × Base Area) + (Base perimeter × height) where "S" is the surface area of the prism.

      What is the formula for the surface area of a rectangle? ›

      Step 1: Multiply the length by the width. Step 2: L X W , where L is the length and W is the width. A square which is also a type of rectangle with all equal sides.

      How do you find the area of the rectangle at the bottom of the rectangular prism? ›

      To find the area of the rectangle, just multiply the two edges together. 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.

      What is the surface area and volume of a prism? ›

      What is important to note is that the surface area of a right prism is the sum of the lateral area, sometimes called the net, and twice the area of a base. And to find the volume of a right prism, we simply find the product of the area of the base and the height of the prism.

      References

      Top Articles
      Latest Posts
      Article information

      Author: Jonah Leffler

      Last Updated:

      Views: 6475

      Rating: 4.4 / 5 (65 voted)

      Reviews: 80% of readers found this page helpful

      Author information

      Name: Jonah Leffler

      Birthday: 1997-10-27

      Address: 8987 Kieth Ports, Luettgenland, CT 54657-9808

      Phone: +2611128251586

      Job: Mining Supervisor

      Hobby: Worldbuilding, Electronics, Amateur radio, Skiing, Cycling, Jogging, Taxidermy

      Introduction: My name is Jonah Leffler, I am a determined, faithful, outstanding, inexpensive, cheerful, determined, smiling person who loves writing and wants to share my knowledge and understanding with you.