Right Prism

A right prism is a prism whose lateral faces are perpendicular to its bases. The 2 bases are congruent, aligned perfectly above one another when the prism rests on its base. In simple words, the angle between any lateral face and any base is a right angle.  In contrast, an oblique prism does not have the lateral faces perpendicular to the bases and thus the 2 bases are not aligned perfectly above one another.

It can be of different shapes such as triangular, rectangular, pentagonal, hexagonal, and trapezoidal. The diagram below shows the difference between a right and an oblique rectangular prism.

Formulas

Surface Area

The surface area of a right prism is the total space occupied by its outermost faces. It is expressed in square units such as cm2, m2, mm2, in2, or yd2.  Surface area of a right prism is of 2 types.

Lateral Surface Area

The lateral surface area (LSA) of a right prism is only the sum of the surface area of all its faces except the bases. The formula to calculate the LSA of a right prism is given below:

Lateral Surface Area (LSA) = Base Perimeter × Height

Total Surface Area

The total surface area (TSA) of a right prism is the sum of the lateral surface area and twice the base area. The formula to calculate the TSA of a right prism is given below:

Total Surface Area (TSA) = (2 × Base Area) + (LSA)

Volume

The volume of a right prism is the total space it occupies in the three-dimensional plane. It is expressed in cubic units such as cm3, m3, in3, ft3, or yd3.

The simple way to find the volume of any right prism is by multiplying its base area with its height (length of the prism or distance between the 2 bases).

The formula to find the volume of a right prism is given below:

Volume (V) = Base Area × Height

Solved Examples

Find the volume and, total and lateral surface area of a right triangular prism whose base area 6 cm2, base perimeter 12 cm, and height is 8 cm.

Solution:

As we know,
Volume (V) = Base Area × Height, here base area = 6 cm2, height = 8 cm
V =  6 × 8
= 48 cm3
Lateral Surface Area (LSA) = Base Perimeter × Height, here base perimeter = 12 cm, height = 8 cm
LSA = 12 × 8
= 96 cm2
Total Surface Area (TSA) = (2 × Base Area) + (LSA), here base perimeter = 12 cm, LSA = 96 cm2
TSA =(2 × 6) + 96
= 108 cm2

Find the volume and lateral surface area of a right rectangular prism whose base area is 18 cm2, base perimeter is 18 cm, and height is 14 cm.

Solution:

As we know,
Volume (V) = Base Area × Height, here base area = 18 cm, height = 14 cm
V = 18 × 14
= 252 cm3
Lateral Surface Area (LSA) = Base Perimeter × Height, here base perimeter = 18 cm, height = 14 cm
LSA = 18 × 14
= 252 cm2

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