How to Find the Volume of a Triangular Prism: Follow This Tutorial to Find the Accurate Result

How to Find the Volume of a Triangular Prism: Follow This Tutorial to Find the Accurate Result
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Tripboba.com - In geometry, a triangular prism is a three-sided prism. It is a polyhedron which comprises of a triangular base, a translated copy, and 3 faces joining corresponding sides. A right triangular prism has rectangular sides to form erectly. A uniform triangular prism is a right triangular prism with equilateral bases and square sides.

You might often bump into maths problems related to this prism. It probably always makes you wonder how to find the volume of a triangular prism. Some might think that we can calculate the volume of a triangular prism the same way we would for a pyramid. 

But remember that a triangular prism is, as mentioned before, a three-sided polyhedron with two parallel triangular bases and three rectangular faces. If you want to find out the volume of a triangular prism, find the area of one of the triangular bases and multiply it by the height of the prism. 

Learn how to find the volume of a triangular prism by following this tutorial.

1. How to Find the Volume of a Triangular Prism: Uniform Polyhedron

A right triangular prism is semiregular or, more generally, a uniform polyhedron. If the base faces are equilateral triangles, the other three faces are squares. This prism can be seen as a truncated trigonal hosohedron, represented by Schläfli symbol t{2,3}. 

Alternately it can be seen as the Cartesian product of a triangle and a line segment, and represented by the product {3}x{}. The dual of a triangular prism is a triangular bipyramid.

The symmetry group of a right 3-sided prism with triangular base is D3h of order 12. The rotation group is D3 of order 6. The symmetry group does not contain inversion.

2. How to Find the Volume of a Triangular Prism: Finding the Area of the Triangle

Start off finding the volume of the triangular prism by identifying the area of the triangle which acts as the base. Find the height and width of the triangle base by looking at the triangle attentively. Write down the base width and height. For example, your triangle might have a base of 8 cm and a height of 9 cm.

You have to be careful when taking note of the values of the properties. Don’t mistake the height you’re currently eyeing with the height of the entire prism. First, you need to identify the base first, so the height here means the height of the triangle, not the prism.

You can use either of the triangular bases, since they should have the same dimensions. If the two bases are asymmetry, then it means the prism is oblique. We’re going to solve problems regarding a basic triangular prism in the first place. This way, the triangular bases in our case are interchangeable.

3. How to Find the Volume of a Triangular Prism: Apply the Formula

Once you’ve identified the height and width of the triangle, what you have to do next is to plug the numbers into the formula. Then, put the numbers into the formula for calculating the triangular area. The following is the formula that you have to apply:

Area = 1/2 x width x height. 

You might also see it written as follows:

V = 1/2 bh

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 the area.

For example, if the base is 8 and the height is 9, you have to calculate it this way using the formula:

V = 1/2 x 8 x 9

Finish the simple calculation and you’ll get the area of the triangle which is 36 cm2.

4. How to Find the Volume of a Triangular Prism

ck12.org - Photo by ck12.org

Once you’ve got the area of the base, now it’s time to learn how to find the volume of a triangular prism. Plug values of the triangular area into the formula to find the volume of the prism. The area of the triangle is 1 of the 2 numbers you need in order to find the prism's volume. 

In the formula V = bh, the triangular area is V = b. By using the earlier example, you’ll get V = 36 x h. You also have to identify the height of the prism in order to find the volume of a triangular prism. The height is the length of 1 of its sides. For example, the prism might be 16 cm long. Place this number in the V = h place of the formula. By using the earlier example, you’ll get V = 36 x 16.

Multiply the triangular area by the height of the prism to find the volume. Since you have completed the equation parts, you just need to multiply the area by the height. The result will be the volume of the triangular prism, which is 576 cm3.

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