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The volume of a triangular prism calculator is an online tool that helps us to calculate the volume of a triangular prism. The volume of a triangular prism can be calculated using the length of the prism, the base length and the height of the triangular base, or, by using the area of the base of the prism and the length of the prism. Now let us familiarize ourselves with the calculator....Read MoreRead Less
Follow these steps to use the volume of a triangular prism calculator:
The volume of a triangular prism is its capacity, or the measure of the amount of space it takes up, and it is measured in cubic units like \({m^3,\ cm^3,}\ in^3,\ ft^3,\) etc.
The volume of a triangular prism \(V\) with a base length \(b\), height of the triangular base \(h\), and the distance between the triangular bases or the length of the prism \(l\), are calculated using the formula:
The volume of triangular prism \(V\) = Base area times length of the prism
= \(\frac{1}{2}\ \times\ (b\times h)\ \times\ l\)
Length of the triangular prism, \(l=\frac{2\times V}{b\times h}\)
Base length of the triangular prism, \(b=\frac{2\times V}{h\times l}\)
Height of the triangular base, \(h=\frac{2\times V}{b\times l}\)
Consider a triangular prism with a base length \(b\), height of the triangular base as \(h\) and length of the triangular prism as \(l\).
The volume of the triangular prism, \(V\) = Base area times length of the prism = \(\frac{1}{2}\ \times\ (b\times h)\ \times\ l\)
On increasing the length by a unit, the new length \(l_1=l+1\)
Hence, the volume of the triangular prism \(V_1=\frac{1}{2}\ \times\ b\times h\ \times\ l_1\)
\(V_1=\frac{1}{2}\ \times\ b\times h\ \times\ (l+1)\)
\(=\frac{1}{2}\ \times\ b\times h\ \times\ l\ +\frac{1}{2}\ \times\ b\times h\)
\(V_1=V+\) Base area
Hence, when the length of a triangular prism is increased by a unit, the volume of the prism increases by an amount that is equal to the triangular base area of the prism.
Example 1:
Determine the volume of a triangular prism with a base altitude of 6 cm, a base length of 3 cm, and if the height of the triangular prism is 8 cm.
Solution:
Given,
b = 3 cm
h = 6 cm
L = 8 cm
The volume of a triangular prism = \(\frac{1}{2}\times(b\times h)\times l\)
= \(\frac{1}{2}\times(3\times 6)\times 8\)
= 72 \(cm^3\)
Example 2:
Find the height of a triangular prism base, if the base length, the prism length, and its volume are 18 yards, 5 yards, and 108 cubic yards, respectively.
Solution:
Given:
Volume, \(V=\ 108\) cubic yards
Base length, \(b=18\) yards
Prism length, \(l=\ 5\) yards
Let the height of the triangular base be \(h\)
Height of the triangular base, \(h=\frac{2\times V}{b\times l}\)
\(h=\frac{2\ \times\ 108}{18\ \times\ 5}\)
\(h\ =\ 2.4\) yards
The height of the triangular base of the prism is 2.4 yards.
Example 3:
Find the length of a triangular prism, if its base length, base height, and volume are 12 inches, 16 inches, and 480 cubic inches respectively.
Solution:
Given:
Volume, \(V=\ 480\) cubic inches
Base length, \(b\ =\ 12\) inches
Height of base, \(h=16\) inches
Let the length of the triangular prism be \(l\)
Length of the triangular prism \(l=\frac{2\times V}{b\times h}\)
\(l\ =\ \frac{480\ \times\ 2}{12\ \times\ 16}\)
\(l=5\) yards
The length of the prism is 5 inches.
Example 4:
Find the base length of a triangular prism, if its prism length, base height, and volume are 16 inches, 18 inches, and 864 cubic inches respectively.
Solution:
Given:
Volume, \(V=\ 864\) cubic inches
Prism length, \(l\ =\ 16\) inches
Height of base, \(h=18\) inches
Let the base length of the triangular prism be \(b\)
Length of the triangular prism \(b=\frac{2\times V}{l\times h}\)
\(b\ =\ \frac{864\ \times\ 2}{16\ \times\ 18}\)
\(b=6\) inches
The base length of the prism is 6 inches.
There are 5 faces (3 lateral faces and 2 identical bases), 9 edges, and 6 vertices that make up a triangular prism.
The two bases of a triangular prism are in the shape of a triangle, while the bases of a rectangular prism are in the shape of a rectangle.
The lateral faces of a triangular prism are parallelograms or rectangular in shape.
A solid shape with four triangular faces, a central vertex point and a single base is called a triangular pyramid. A triangular prism, on the other hand, is a polyhedron with two congruent triangular bases, and the rest of the 3 faces are parallelograms or rectangular. As a result, a pyramid is not the same as a triangular prism.
A right triangular prism has a 90-degree angle formed by the edges of the triangular bases.
The formula for calculating the volume of a triangular prism is Volume = base area × prism length. Hence, the volume of a triangular prism is length times the base area.
Volume of a triangular prism = 1/3×b×h×l, where b is the base length of the triangle, h is its height, and l is the distance between its bases. Therefore, from the above relation we can observe that the volume of a triangular prism does not depend on the angle of the triangular base.