How to Calculate the Volume of a Triangular Prism

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Calculating the volume of a triangular prism is often easily assumed to be the same as calculating the volume of a pyramid. However, a triangular prism is a three-sided polyhedron with two triangular parallel bases and three rectangular faces. To calculate the volume of a triangular prism, you simply find the area of one of the bases of the triangle and multiply it by the height of the prism.

Table of Contents

Find the area of triangle

Image titled Calculate the Vpume of a Triangular Prism Step 1

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Find the height and length of the base of a triangle. Look at the triangle and write down the length of its base and its height. For example, your triangle has a base side of 8 cm and a height of 9 cm. ^{[1] X Research Source}

Remember that you are specifying the height of the triangle , not the height of the prism.
You can use either triangle of the base of the prism since they are the same size.

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Image titled Calculate the Vpume of a Triangular Prism Step 2

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Substitute the numbers into the formula to find the area of a triangle. Once you know the length of the base and the height of the triangle, you will substitute these numbers into the formula to calculate the area of the triangle: ^{[2] X Research Source}

Area = 1/2 x base length x height. You can also see the formula written as $DRAW$ $=$ $first$ $2$ $b$ $H$ ${displaystyle V={frac {1}{2}}bh}$ ${displaystyle V={frac {1}{2}}bh}$

Image titled Calculate the Vpume of a Triangular Prism Step 3

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Multiply 1/2 by the length of the base and multiply by the height to calculate the area of the triangle. To find the area of the base triangle of the prism, you would multiply the length of the base by the height and multiply by 1/2. Remember to write your results in squared units because you are calculating area. ^{[3] X Research Sources}

For example, if the base length is 8 and the height is 9, your calculation would be $DRAW$ $=$ $first$ $2$ $*$ $8$ $*$ $9$ ${displaystyle V={frac {1}{2}}*8*9}$ ${displaystyle V={frac {1}{2}}*8*9}$ . The area of the triangle is 36 cm ² .

Find the volume of the prism

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Substitute the area value of the triangle into the formula to find the volume of the prism. The area of the triangle is one of two numbers you need to find the volume of the prism. In the formula

DRAW

=

b

H

{displaystyle V=bh}

{displaystyle V=bh}

, the area of the triangle is

DRAW

=

b

{displaystyle V=b}

{displaystyle V=b}

. ^{[4] X Research Sources}

For the example above, the formula would be $DRAW$ $=$ $36$ $*$ $H$ ${displaystyle V=36*h}$ ${displaystyle V=36*h}$ .

Image titled Calculate the Vpume of a Triangular Prism Step 5

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Determine the height of the prism and substitute the formula. Now you need to find the height of the triangular prism, i.e. the length of one of the sides. For example, a prism has a height of 16 cm. You would substitute this number in the formula

DRAW

=

H

{displaystyle V=h}

{displaystyle V=h}

. ^{[5] X Research Sources}

For example, your calculation will now be $DRAW$ $=$ $36$ $*$ $16$ ${displaystyle V=36*16}$ ${displaystyle V=36*16}$ .

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Multiply the area of the triangle by the height of the prism to find the volume. Since you now have all the components of the equation, you will multiply the area of the base of the triangle by the height of the prism. The result will be the volume of the triangular prism. ^{[6] X Research Source}

Thus, if $DRAW$ $=$ $36$ $*$ $16$ ${displaystyle V=36*16}$ ${displaystyle V=36*16}$ , the answer would be 576 cm ³ .

Advice

Be sure to use the same unit of measure for all prismatic measurements before calculating. For example, if some measurements of a prism are in millimeters and the rest are in centimeters, you need to convert millimeters to centimeters first.

Steps

Find the area of triangle

Find the volume of the prism

Advice

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