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How to Calculate Surface Area & Volume of a Triangle

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.

Things You'll Need

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Instructions

    • 1

      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.

    • 2

      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.

    • 3

      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.

    • 4

      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.

    • 5

      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.

    • 6

      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.

    • 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.

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