Volume of a Triangular Prism Calculator | Free Online Volume of a Triangular Prism Calculator with Steps - BYJUS

# Volume of a Triangular Prism Calculator

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

## Online Volume of a Triangular Prism Calculator

### How does the Volume of a Triangular Prism Calculator work?

Follow these steps to use the volume of a triangular prism calculator:

1.  Enter the known measures (i.e., any three out of volume of the triangular prism, the length of the prism, the base length, and the height of the triangular base) into the respective input boxes and the unknown measure will be calculated.
2. Select the appropriate units for the input and output..
3. Now, click on ‘Solve’ to obtain the result.
4. Click on the ‘Show Steps’ button to know the stepwise solution to find the missing measure.
5.  Click on the  button to enter new inputs and start again.
6. Click on the ‘Example’ button to play with different random input values.
7. Click on the ‘Explore’ button to see how the base area and volume of a triangular prism changes with a change in its dimensions. You can also change the angle of the triangular base by moving the slider. Try it out!
8. When on the ‘Explore’ page, click the ‘Calculate’ button if you want to go back to the calculator page.

### What is the Volume of a Triangular Prism?

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.

### Formulas used for the ‘Volume of Triangular Prism’ Calculator

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, $$h=\frac{2\times V}{b\times l}$$

### How does the Volume change with a unit increase in Length of the Prism?

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.

### Solved Examples:

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.