How to Find Surface Area of a Cube and a Rectangular Prism

How to Find Surface Area of a Cube and a Rectangular Prism
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  • 0:01 Rectangular Prisms & Cubes
  • 0:44 Surface Area Formula
  • 1:48 For a Rectangular Prism
  • 3:23 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video lesson, you will be able to use the formula for the surface area of a rectangular prism. You will know what measurements you need to use it and how you can apply it to a cube as well.

Rectangular Prisms and Cubes

Imagine that you are a gift wrapper at a big store. Customers give you boxes of all sizes to wrap up nicely. These boxes are in the shape of a rectangular prism. All the sides of a rectangular prism are rectangles, and all the sides meet at a perpendicular angle.

Sometimes you get a rectangular prism where all the sides are equal. A box like that is in the shape of a cube. As the gift wrapper, your job is to make sure that you completely cover each gift box with some nice wrapping paper. To help you do this, you calculate the surface area, the outside area, of each box before you begin. This way, you are able to cut a piece of wrapping paper big enough to cover your box.

Surface Area Formula

Since all your boxes are rectangular prisms, you use the formula for the surface area of a rectangular prism for all your boxes, even your cubes! This formula tells you the surface area is equal to twice the product of the width and the length plus twice the product of the length and height plus twice the product of the height and width.

surface area of rectangular prism

What is going on in this formula? It is calculating the area of each side and then adding them all up. You have a total of 6 sides to your box. Your opposite sides are always equal to each other in your cube. Looking at the formula, we see that the first term, 2wl, is the area of the top and bottom faces of the box together; 2lh is the area of the front and back faces of the box; and 2hw is the area of the left and right faces of the box. If you happen to forget this formula, just remember to find the area of each face and then add them all up.

For a Rectangular Prism

Your workday has officially started now. Your first customer gives you a lengthy package, a rectangular prism. Its dimensions are 10 inches long by 3 inches wide by 3 inches high. It's a long box, so perhaps there is a rose inside. You need to calculate the surface area so you know how much wrapping paper you need. From the dimensions, you know that the l is 10, the w is 3, and the h is also 3. Plugging these into the formula, we have 2 times 3 times 10 plus 2 times 10 times 3 plus 2 times 3 times 3.

surface area of rectangular prism

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