8th Grade Math Help: Finding the Surface Area of a Prism

In middle school, you'll learn to find the surface area of 3-dimensional shapes, including rectangular, triangular and irregular prisms. Read on for instructions and examples!

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Surface Area for Prisms

A prism is a 3-dimensional shape with two parallel bases that are congruent. The prism's base may be square, rectangular, triangular or irregular. Since there are so many different types of prisms, there is no single surface area formula for them all. However, you can find the surface area of any prism by following these general steps:

  1. Find the area of the prism's base by using the appropriate area formula. For example, if the prism's base is rectangular, you'll use the formula 'length x width.'
  2. Multiply the area of the base by two, since there are two bases.
  3. Find the surface area of the prism's sides. To calculate this, you'll need to multiply the perimeter of the prism's base by its height.
  4. Add together the areas of the prism's bases and sides. This will give you the prism's total surface area.

Surface Area Formulas

There are some types of prisms that you'll encounter frequently. Here are the instructions for finding their surface areas.

Rectangular Prism

A rectangular prism has two rectangular bases. The formula for finding the surface area of a rectangular prism is 2LW + 2(L + W)h. Here's how to calculate it:

  1. To find the area of one of the bases, multiply its length (L) by its width (W). Then, multiply the result by two.
  2. Calculate the perimeter of the base using the formula 2(L + W). In other words, add together the length and width of the base, and then multiply that result by two.
  3. Multiply the perimeter of the base by the prism's height.
  4. Add together the results of step one and step three.

Triangular Prism

If your prism has two triangular bases, then you're dealing with a triangular prism. The formula to calculate its surface area is bh + (S1 + S2 + S3)h. To apply the formula, follow these steps:

  1. To get the combined area of the two bases, multiply the base (b) and the height (h) of one of them. You don't need to multiply by two, since the formula for the area of a single base is 1/2bh.
  2. Calculate the perimeter of the triangular base by adding the lengths each of the three sides (S1 + S2 + S3).
  3. Multiply the result of step two by the height of the prism.
  4. Add the results of steps one and three to get the prism's surface area.

Cylinders

Although they're usually called cylinders, 3-dimensional shapes with parallel, circular bases fit the definition of a prism. The formula for finding their surface area is 2(pi)r^2 + 2(pi)rh. Here are the steps you follow to use it:

  1. Use the formula (pi)r^2 to find the area of the base. This means that you multiply pi (3.14) by the base's radius squared (r^2).
  2. Multiply the result of step one by the number two, since there are two bases.
  3. Find the perimeter of the base by using the formula 2(pi)r.
  4. Add the result of step three to the result of the second step. The answer is your cylinder's surface area.
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