Formula for the Volume of a Triangular Prism
The formula for the volume of a triangular prism is given by,
V = B x h, where B is the base area and h is the height.
The term ‘B’ is the base area and this can be calculated as,
\(B=\frac{1}{2}~\times~base~\times~height~of~the~triangle\).
Hence, the volume of a triangular prism can also be written as,
\(V=\frac{1}{2}~\times~base(a)~\times~height(c)~\times~prism~height(h)\) cubic units.
⇒ \(V=\frac{1}{2}~\times~a~\times~c~\times~h\) cubic units.
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Solved Examples
Example 1: Find the volume of a triangular prism with a base area of 12 \(cm^2\) and with a height of 6 cm.
Solution :
As provided in the question,
The base area, B = 12 \(cm^2\)
Height, h = 6 cm
According to the volume of triangular prism formula,
V = B x h
By substituting the values,
V = 12 x 6
V = 72 \(cm^3\)
So, the volume of the triangular prism is 72 cubic centimeters.
Example 2: Determine the volume of a triangular prism in which the base of the triangle is 8 inches, the height is 6 inches and the length of the prism is 12 inches.
Solution: Details that are stated,
The base of the triangle, a = 8 inches
Height of the triangular base, c = 6 inches
So, the base area \(B=\frac{1}{2}~\times~base~(a)~\times~height~(c)\)
\(B=\frac{1}{2}~\times~8~\times~6\)
\(B=\frac{48}{2}\)
B = 24 \(in^2\)
Length of the prism or height of the prism, h= 12 inches
According to the formula for the volume of a triangular prism,
V = B x h
V = 24 x 12
V = 288 \(in^3\)
Hence, the volume of the triangular prism is 288 cubic inches.
Example 3: Amanda bought a triangular prism as a paper weight. The altitude of the base is 5 cm, edge length is 8 cm, and height of the prism is 6 cm. Find the volume of this triangular prism.
Solution :
Provided in the question is,
a = 8 cm c = 5 cm, h = 6 cm
According to the formula,
Volume of triangular prism V = \(\frac{1}{2}~\times~a~\times~c~\times~h\)
V = \(\frac{1}{2}~\times~8~\times~5~\times~6\)
V = \(\frac{1}{2}~\times~240\)
V = 120 \(cm^3\)
So, the volume of the triangular prism that Amanda bought is 120 cubic centimeters.
The volume of a triangular prism is defined as the space inside it. The volume of a triangular prism can be derived by multiplying the area of the triangular base and the height of the prism(or the length of the prism).
The formula for the volume of a rectangular prism is given by, Volume = l × w × h, where l is the length, w is the width, and h is the height of the prism.
The volume of a solid shape helps us to know the capacity of an object. By learning about the volume of any object, we will be able to understand the quantity of something required to fill that particular solid shape.
The standard unit for measuring volume is a value that is expressed in a cubic format. There are other units as well for measuring large or small quantities of volume.
The units for measuring length according to the English or Customary system are the inch, foot, yard, and mile.