How to Calculate a Prism

By Richard Rowe
Spectrophotometers use prisms to aid in the UV capabilities of a device.
prism image by pncphotos from Fotolia.com

A prism is a geometrical shape defined as having a top and bottom made up of a regular shape -- often a triangle, square, octagon or hexagon -- and straight sides connecting the top and bottom. Think of a refrigerator box with a square top and square bottom and you've got the idea. Calculating the volume of any prism is as simple in principle as finding the volume of a cylinder, which is just a round prism; you multiply the base shape volume by the height. The extra step comes in finding the volume of the base shape.

Determine the base area of a square or rectangular-shaped prism by multiplying length times width. For example, a square base measuring 4 inches on one side comes out to 16 square feet -- 4 times 4 equals 16.

Determine the base area of a triangular prism by figuring out what its area would be if it were a square or rectangle, and then divide by two. A triangle is half of a square. For example, a triangle measures 2 inches on its base and 3 inches from its peak to the base. Calculate that as a square and you get 6 square inches; divide that by two to get 3 square inches of area for the triangle.

Determine the area of any regular polygon with more than four sides -- pentagon, hexagon, octagon or any other of higher side count -- by finding the apothem and the perimeter. Find the perimeter by adding together the lengths of the shape's sides, or by multiplying the length of one side by the number of sides if it's a regular shape. The apothem is a line that starts at the exact center of the polygon drawn so that it hits one of the sides at a 90-degree angle. To get the area of any regular polygon, multiply the apothem by the perimeter, then divide it by half. The formula is A = Pa x 1/2.

For example, take a pentagon with five sides measuring 2 inches each, for a perimeter of 10 inches. If the apothem is 5 inches, multiply 5 times 10 and multiply by one-half to equal 25 square inches.

Calculate the total volume of the prism by multiplying your base shape's volume by the height. If you use a height of 5 inches, the total area of the square prism in Step 1 equals 80 cubic inches -- 16 times 5 equals 80. The triangular prism in Step 2 equals 15 cubic inches -- 3 times 5 equals 15. The pentagram in Step 3 equals 125 cubic inches -- 25 times 5 equals 125.

About the Author

Richard Rowe has been writing professionally since 2007, specializing in automotive topics. He has worked as a tractor-trailer driver and mechanic, a rigger at a fire engine factory and as a race-car driver and builder. Rowe studied engineering, philosophy and American literature at Central Florida Community College.