Finding the Volume of a Triangular Prism

In geometry, a triangular prism or three-sided prism is a type of prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.

Types of triangular prisms

• Equilateral triangular prism - with equilateral triangle as it's base.
• Isosceles triangular prism - with isosceles triangle as it's base.
• Scalene triangular prism - with scalene triangle as it's base.
• Right triangular prism - With equilateral triangle as it's base and other three faces are squares.

Here we are going to learn finding the volume of a triangular prism. (Source: From Wikipedia).

Formula for finding the volume of a triangular prism

The volume of a triangular prism can be found by the product of the base area and the height of the triangular or the distance between the bases.
Volume of a triangular prism = (base area * height of the prism) cubic units.

The formula for finding the volume of the triangular prism changes with the type of base triangle. So we will have different formulas according to the type of base triangle.
So, the volume of a triangular prism is just given as, V = (base area * height or distance between the base) cubic units.

Example problems to finding the volume of a triangular prism

Example 1
Find the volume of a triangular prism with the given dimensions; the base of the triangle is 4 cm and the height of the triangle is 5 cm. The distance between the base triangles is 15 cm.
Solution
The volume of a triangular prism = (base area * height of the prism) cubic units.
Here, the base area = area of triangle = `1/2 bh`
Given that, b = 4 cm and h = 5 cm.
Area of the base triangle = `1/2` * 4 * 5
                                             = 10 square cm.
The volume of the triangular prism = 10 square cm * distance between the base triangles
                                                               = 10 * 15
                                                               = 150 cubic cm
So the volume of the given triangular prism is 150 cubic cm.


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Example 2
Find the volume of a triangular prism with all sides equal to 4 cm.
Solution
The given triangular prism is a right triangular prism (equilateral triangle as base and all other faces are squares).
For finding the volume of the triangular prism, first we have to find the area of the base triangle.
As the base triangle is an equilateral triangle (equal sides), the area = `sqrt(3)/4 s^2` square units.
Area of the base = `sqrt(3)/4 4^2`
                               = `sqrt(3)/4` * 4 * 4
                               = `sqrt(3)` * 4
                               = `4sqrt(3)`
Volume of the triangular prism = `4sqrt(3)` * 4
                                                        = `16sqrt(3)`
The volume of the given triangular prism is `16sqrt(3)` cubic units.