How to Calculate Surface Area & Volume of a Triangle

By Kate Bruscke
Area and volume problems are common in geometry.
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Area is a numerical expression which tells you how much surface a two-dimensional shape, such as a triangle, holds in a plane. Area is useful when determining how much material, such as paint or carpeting, is needed to cover a specific section or location. Volume, on the other hand, expresses the amount of space a three-dimensional shape, such as a pyramid, can contain within itself -- a measurement needed to understand the holding capacity of a container, for example. Both area and volume are calculated using formulas.

Locate the values for the base (b) and height (h) of a triangle in order to determine its area (a). For example, you may be given a triangle with a base of 5 and a height of 4.

Multiply the base by the height, and then multiply by 1/2 to determine the area. The formula for the area of a triangle is a = 1/2 bh. To find the area in the example triangle, plug in 1/2 5(4) to get an area of 10.

Use the formula for area of a triangle to determine the area for each pyramid (three-dimensional triangle) face. Add up these areas to find the sum. Using the example, each pyramid face has a base of 5 and a height of 4, giving an area of 10. If the pyramid has 3 faces, add 10 + 10 + 10 to get 30.

Calculate the area of the pyramid's base, which is usually a square, by locating the values for the base (b) and height (h) -- the same value in a square -- and then multiplying the base by the height to determine the area. The formula for the area of a square is a = bh. If your example pyramid has a base and height of 5, plug in 5(5) to get an area of 25.

Add the area of the base to the sum of the areas of the pyramid faces to find the surface area of the pyramid. In the example, 30 + 25 equals a surface area of 55.

Locate the values for the base (b) and height (h) of a pyramid in order to determine its volume (v). For example, a pyramid has a base of 3 and a height of 7.

Multiply the base by the height, and then multiply by 1/3 to determine the volume. The formula for the volume of a pyramid is v = 1/3 bh. For the example, plug in 1/3 3(7) to give a volume of 7.

About the Author

A writer and professional lab assistant based in Seattle, Kate Bruscke has been writing professionally about health care and technology since 1998. Her freelance clients include "The Seattle Times," KGB.com, Reading Local: Seattle, Nordstrom and MSN/Microsoft. Bruscke holds a Master of Fine Arts from The School of the Art Institute of Chicago.