Rectangular Prism

A prism can be defined as a solid figure with identical bases and some cross-section as we move along its length. A prism is classified into various types based on the bases of the prism. For instance, if the base of a prism is triangular, then it is known as a triangular prism. Similarly, when the base of the prism is rectangular, it is known as the rectangular prism. It is made up of six faces, twelve edges, and 8 vertices. We shall discuss the volume of a rectangular prism, differences from a triangular prism, and many more.

Volume of Rectangular Prism

The volume of a rectangular prism is the area or space that is occupied inside it. Mathematically the volume of a rectangular prism is the product of length, breadth, and height or l * b * h.
Note: The resultant value is always written in cubic units. Some of the examples based on the volume of a rectangular prism are mentioned below.

Example 1: Find the volume of the rectangular prism if the length, breadth, and height are equivalent to 6 cm, 8 cm, and 10 cm respectively.

Solution:

                 Given that,

                 Length of the rectangular prism = 6 cm

                 The breadth of the rectangular prism = 8 cm

                 Height of the rectangular prism = 10 cm

                 Using the formula = l * b * h.

                 6 cm * 8 cm * 10 cm = 80 * 6

                 80 * 6 = 480 cm cubic units.

                 Hence, the volume of the rectangular prism is 480 cm cubic units.

Rectangular Prism Vs Triangular Prism

The following points mentioned below analyze the differences between a rectangular prism and a triangular prism.

  1.  A polyhedron with two rectangular bases and three triangular faces is known as a rectangular prism whereas a three-dimensional shape with six rectangular faces arranged in a way that all of them are congruent to each other is known as a rectangular prism.
  2.  The volume of a rectangular prism is the product of length, breadth, and height or l * b * h. Likewise, the volume of a triangular prism it’s half of the product of its length, breadth, and height. Mathematically, 1/2 * b * l * h.
  3.  Common fact: The resultant value for the volume of both figures is written in cubic units and thus both of them are considered as a three-dimensional shape.

Triangular Prism

A prism with triangular bases can be defined as a triangular prism. However, it is made up of three rectangular lateral faces. Base signifies the bottom of the prism whereas the faces signify the top of the prism. To identify a triangular prism, one must be aware of its properties. The properties of a triangular prism are:

  1.  A triangular prism is made up of 5 faces, 6 vertices, and 9 edges.
  2.  It is also regarded as a polyhedron with two rectangular faces and two faces that are triangular.
  3.  The cross-section of any triangular prism will form a triangle.

Volume of Triangular Prism

To recall, the volume of the triangular prism is the total region that is occupied by the prism inside it. Mathematically, the volume of the triangular prism is written like half of the product of its length, breadth, and height or 1/2 * b * l * h. 

Example 1: Find the volume of a triangular prism if the length, breadth, and height of the prism are 2 cm, 4 cm, and 6 cm respectively?

Solution:
                  Given that,

                  Length of the triangular prism = 2 cm

                  The breadth of the triangular prism = 4 cm

                  Height of the triangular prism = 6 cm

                  Using the formula, 1/2 * l * b * h.

                  1/2 * 2 * 4 * 6 = 1/2 * 24.

                  1/2 * 24 cm = 12 cm cubic units.

                  Hence, the volume of the triangular prism = 12 cm cubic units.

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