About Volume of Triangular Prism
What is a Triangular Prism?
A polyhedron with two triangular bases and three rectangular sides is referred to as a triangular prism. It is a three-dimensional object with two bases and three lateral faces that are joined by edges. It is referred to as the right triangular prism if the sides are rectangular; otherwise, it is referred to as an oblique triangular prism. It contains 5 faces, 6 vertices, and 9 edges altogether.
Volume of a Triangular Prism
Volume is the amount of space occupied by a solid. Here the volume of a triangular prism is equal to the number of unit cubes that can be filled in it. To calculate the volume of the triangular prism, multiply the area of the base by the height of the prism.
Formulation
It is expressed using cubic units like \(cm^3,m^3,in^3\).
Volume of a triangular prism = Area of base triangle × Length of the prism
Area of base = \(\frac{1}{2}\) × b × h
And length of prism = l
So, Volume of Triangular Prism = \(\frac{1}{2}\) × b × h × l
where ‘b’ is the base length, ‘h’ is the height of a triangular base, and ‘l’ is the height of the prism.
Solved Examples
Example 1: Find the volume of a triangular prism with the following measurements: 19 centimeters as the base, 11 centimeters as the height, and 26 centimeters as the length of the prism.
Solution:
Base of the triangle is b = 19 cm
Height of the triangular base h = 11 cm
Length of the prism is l = 26 cm
V= \(\frac{1}{2}\) × b × hl [Write the formula]
V = \(\frac{1}{2}\) × 19 × 11 × 26 [Substitute the values]
V = \(\frac{1}{2}\) × 5434 [Multiply]
V = 2717 \(cm^3\) [Divide]
Hence, the volume of the triangular prism is 2717 cubic centimeters.
Example 2: Find the volume of a triangular prism with a base measurement of 6 inches, a height of 4 inches, and a length of 16 inches.
Solution:
As stated in the question,
Base of the triangle is b = 6 in
height of the triangular base h = 4 in
length of the prism is l = 16 in
V = \(\frac{1}{2}\) × b × hl [Write the formula]
V = \(\frac{1}{2}\) × 6 × 4 × 16 [Substitute the values]
V = \(\frac{1}{2}\) × 384 [Multiply]
V = 192 \(in^3\) [Divide]
Hence, the volume of the triangular prism is 192 cubic inches.
Example 3: Calculate the volume that a tent would occupy with a base of 2.5 meters, a height of 3 meters, and length of tent 4 meters.
Solution:
Base of the triangle is b = 2.5 m
Height of the triangular base h = 3 m
Length of the prism is l = 4 m
V = \(\frac{1}{2}\) × b × hl [Write the formula]
V = \(\frac{1}{2}\) × 2.5 × 3 × 4 [Substitute]
V = \(\frac{1}{2}\) × 30 [Multiply]
V = 15 \(m^3\) [Divide]
Hence, the volume occupied by the camping tent is 15 cubic meters.
A triangular prism has five faces: three lateral faces and two bases.
Six vertices make up a triangular prism, three on each of the triangular faces.
The height of a triangular prism can be calculated by dividing the volume by the area of its triangular base.
The inside space of a triangular prism is its volume. It is computed by multiplying the height of a prism with the area of its triangular base. Volume is expressed in cubic units like cubic inches, cubic feet, and cubic centimeters.