Calculate the Volume of a Triangular Prism

In math, a triangular prism is a three-sided polyhedron with two parallel triangular bases and three rectangular faces. It should not be confused with a pyramid. If you want to calculate the volume of a triangular prism, all you have to do is find the area of one of the triangular bases and multiply it by the height of the shape.

Steps

  1. Identify the base and height of one of the triangular bases. The triangular bases of the triangular prism will have the same dimensions, so it doesn't matter which triangle you use. Now, find the base and the height of the triangle by locating the length of one of the sides of the triangle as well as the length of a line perpendicular to that first line. If you're working with a right triangle, then great -- you can just take the length of the two sides.
    • Let's say you're working with a triangle with a height of 3 cm and a base of 4 cm.
  2. Multiply them. This is the first step to finding the area of the base, which is in the case of the triangular prism, a triangle. So: 3 cm x 4 cm = 12 cm 2. Don't forget to state your answer in square units since you're working with area.
  3. Divide the result by two. To finish finding the area of the triangular base, simply divide 12 cm2 by 2. So, 12 cm2/2 = 6 cm2
  4. Multiply this number by the height of the shape. Let's say the height of the triangular prism, or the length of one of its sides, is 10 cm. So, just multiply 6 cm2 x 10 cm to find the volume of the triangular prism. 6 cm2 x 10 cm = 60 cm3. Don't forget to state your answer in cubic units since you're working with volume.
    • You have just followed the simple formula for finding the volume of a triangular prism: 1/2 x bh x l.



Tips

  • The formula to calculate the volume of a triangular prism is equal to B times H, or Base times Height. To find the base, multiply the length by the width and divide that by 2.
  • Take the bases area and multiply by the height.
  • In all regular pyramids, the slant height, edge height, and edge length are also related by the Pythagorean theorem: (edge ÷ 2)2 + (slant height)2 = (edge height)2

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