8th Grade Math Help: Finding the Surface Area of a Prism
In middle school, you'll learn to find the surface area of 3dimensional shapes, including rectangular, triangular and irregular prisms. Read on for instructions and examples!
Surface Area for Prisms
A prism is a 3dimensional 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:
 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.'
 Multiply the area of the base by two, since there are two bases.
 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.
 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:
 To find the area of one of the bases, multiply its length (L) by its width (W). Then, multiply the result by two.
 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.
 Multiply the perimeter of the base by the prism's height.
 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:
 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.
 Calculate the perimeter of the triangular base by adding the lengths each of the three sides (S1 + S2 + S3).
 Multiply the result of step two by the height of the prism.
 Add the results of steps one and three to get the prism's surface area.
Cylinders
Although they're usually called cylinders, 3dimensional 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:
 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).
 Multiply the result of step one by the number two, since there are two bases.
 Find the perimeter of the base by using the formula 2(pi)r.
 Add the result of step three to the result of the second step. The answer is your cylinder's surface area.
Other Articles You May Be Interested In

This article outlines steps that parents of elementary school children can take to assist their student in learning and mastering the fundamentals of English grammar and writing.

How useful is homework? Read on to learn about the different types of homework and how it can be applied most successfully to a student's education.
We Found 7 Tutors You Might Be Interested In
Huntington Learning
 What Huntington Learning offers:
 Online and incenter tutoring
 One on one tutoring
 Every Huntington tutor is certified and trained extensively on the most effective teaching methods
K12
 What K12 offers:
 Online tutoring
 Has a strong and effective partnership with public and private schools
 AdvancEDaccredited corporation meeting the highest standards of educational management
Kaplan Kids
 What Kaplan Kids offers:
 Online tutoring
 Customized learning plans
 RealTime Progress Reports track your child's progress
Kumon
 What Kumon offers:
 Incenter tutoring
 Individualized programs for your child
 Helps your child develop the skills and study habits needed to improve their academic performance
Sylvan Learning
 What Sylvan Learning offers:
 Online and incenter tutoring
 Sylvan tutors are certified teachers who provide personalized instruction
 Regular assessment and progress reports
Tutor Doctor
 What Tutor Doctor offers:
 InHome tutoring
 One on one attention by the tutor
 Develops personlized programs by working with your child's existing homework
TutorVista
 What TutorVista offers:
 Online tutoring
 Student works oneonone with a professional tutor
 Using the virtual whiteboard workspace to share problems, solutions and explanations