## Volume of a Triangular Prism

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Like it? Share it! Calculating the volume and surface area of regular solid objects is one of the fundamentals of solid geometry. In this article, we’ll focus on how to calculate the volume of a triangular prism…

The volume of an object is defined by the amount of 3-dimensional space enclosed by it. For an object to have volume, it must have 3 dimensions, i.e., length, breadth, and height. Two-dimensional objects are considered to have zero volume. The volume is measured by the quantity of fluid that the object can hold. The unit of volume is cubic meter or m3. In mathematics, we have formulas to calculate the volume of three dimensional solids of different shapes. The most common solids include spheres, pyramids, cubes, cuboids, cones, cylinders and prisms.

In geometry, a polyhedron is defined as a solid made up of sides known as faces, where each face is a polygon (a 2-dimensional shape enclosed by straight lines). A prism is an example of a polyhedron. The following is the definition of a prism.

A prism is a polyhedron in which the top and bottom faces (bases) are congruent polygons and the sides are parallelograms, and which has the same cross section throughout its entire length.

This means that both the bases of a prism are similar in shape and dimensions. A prism is named by the shape of its cross section. For example, if the cross section of the prism is a polygon with three sides, the prism is called a triangular prism. Similarly, we can have square, pentagonal, hexagonal, heptagonal, octagonal, nonagonal or decagonal prisms as well. A triangular prism is, thus, a prism in which the top and bottom faces are triangles.

### Calculating the Volume of a Triangular Prism

The volume of a prism, in general, is obtained by multiplying the area of the base of the prism, with the distance between the two bases (or height) of the prism. This is given by the formula:

Volume of a prism = Area of the base of the prism x height of the prism
or,
V = Bl
where B is the area of the base and l is the height of the prism.

For a triangular prism, the formula for calculating the volume is as given below.

V = ½ bhl

where V is the volume of the triangular prism, b is the base of the triangle, h is the height of the triangle and l is the height of the prism (as shown in the diagram).

While calculating the volume of a triangular prism, or using the volume formula for any other geometrical shape, make sure that all the measurements are in the same unit. If not, then convert the units using proper methods of conversion. However, if you find that the given measurements are in terms of three or more units, calculate the volume after converting all of them to the S.I. unit of length, i.e., meter (m).

Now, that you have the formula for calculating the volume of a triangular prism, just try to solve a couple of simple problems, which will help you get a hang of it. Once you are done, you can click to know the solutions.

Problem 1
Consider a triangular prism with 20 cm as the length of the base, 15 cm as the height of the base and 35 cm as the distance between its two bases. Find the volume of the prism.