How to find the volume of a right triangular prism

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This page examines the properties of a triangular prism.

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Triangular Prism Volume Formula
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Triangular Prism Volume Formula

The volume of a triangular prism can be found by multiplying the base times the height.

Both of the pictures of the Triangular prisms below illustrate the same formula. The formula, in general, is the area of the base (the red triangle in the picture on the left) times the height, h. The right hand picture illustrates the same formula.

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It's easy to assume that you'd calculate the volume of a triangular prism the same way you would for a pyramid. However, a triangular prism is a three-sided polyhedron with two parallel triangular bases and three rectangular faces. To calculate the volume, all you have to do is find the area of one of the triangular bases and multiply it by the height of the prism.

1
Find the height and width of a triangle base. Look at the triangle and write down the base width and height. For example, your triangle might have a base of 8 cm and a height of 9 cm.[1]
- Keep in mind that you're identifying the height of the triangle, not the entire prism.
- You can use either of the triangular bases, since they should have the same dimensions.
2

Plug the numbers into the formula to find the triangular area. Once you know the width and height of the triangle, put the numbers into the formula for calculating triangular area:[2]
- Area = 1/2 x width x height. You might also see it written as
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3
Multiply 1/2 by width by height to get the area of the triangle. In order to find the area of the triangular base for the prism, multiply the width by the height by 1/2. Remember to put the answer in square units because you're calculating area.[3]
- For example, if the base is 8 and the height is 9, your formula will look like . The area of the triangle is 36 cm 2.

1
2
Identify the height of the prism and put it in the formula. Now you need to find the height of the triangular prism, which is the length of 1 of its sides. For example, the prism may be 16 cm high. Place this number in the place of the formula.[5]
- For example, your formula should now look like .
3

Multiply the triangular area by the height of the prism to find the volume. Since you now have all the parts of the equation, multiply the area by the height. The result will be the volume of the triangular prism.[6]
- So, if , the answer is 576 cm 3.

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Question
How do I calculate the area of a triangular prism?

To find the surface area of a triangular prism, you would find the area of all the faces, then add them together.
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How can I find the volume of a rectangular prism?

To find the volume of a rectangular prism, multiply the prism's width, height, and length. V = w*h*l
Question
How do I find the volume of a square pyramid?

V = (1/3)(s²)(h), where s is the length of a side of the base, and h is the height.

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Ensure that the units of measurement are the same for all parts of the triangular prism before you begin the calculation. For example, if 1 part of the prism is in millimeters and the rest is in centimeters, convert the millimeters to centimeters first.
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To calculate the volume of a triangular prism, first you need to find the area of one of the triangular bases by multiplying ½ by the base of the triangle and by the height of the triangle. For example, if the base is 8 and the height is 9, you would get ½ x 8 x 9 = 36. Therefore, the area is 36. Next, plug the area into the formula for finding the volume of a triangular prism, which is V = b x h, or volume equals the area of the base multiplied by the height of the prism. Now, plug the height of the prism into the formula and solve. As an example, if the area of the triangular base is 36 and the height of the prism is 16, you would get 36 x 16 = 576. Therefore, the volume of the triangular prism is 576. Write your answer in cubic units. If you want to learn how to calculate the height of a regular triangle, keep reading!

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