Table of Contents

Last modified on August 3rd, 2023

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.

The surface area of a right prism is the total space occupied by its outermost faces. It is expressed in square units such as cm^{2}, m^{2}, mm^{2}, in^{2}, or yd^{2}. Surface area of a right prism is of 2 types.

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**

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)**

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 cm^{3}, m^{3}, in^{3}, ft^{3}, or yd^{3}.

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**

**Find the volume and, total and lateral surface area of a right triangular prism whose base area 6 cm ^{2}, base perimeter 12 cm, and height is 8 cm.**

Solution:

As we know,

Volume* (V) = *Base Area × Height, here base area = 6 cm^{2}, height = 8 cm

∴ *V* = 6 × 8

= 48 cm^{3}

Lateral Surface Area (*LSA*) = Base Perimeter *× *Height, here base perimeter = 12 cm, height = 8 cm

∴ *LSA *= 12 × 8

= 96 cm^{2}

Total Surface Area (*TSA*) = (2 × Base Area) + (*LSA*), here base perimeter = 12 cm, *LSA *= 96 cm^{2}

∴ *TSA *=(2 × 6) + 96

= 108 cm^{2}

**Find the volume and lateral surface area of a right rectangular prism whose base area is 18 cm ^{2}, 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 cm^{3}

Lateral Surface Area (*LSA*) = Base Perimeter *× *Height, here base perimeter = 18 cm, height = 14 cm

∴ *LSA* = 18 × 14

= 252 cm^{2}

**More Resources:**- Volume of a Prism
- Surface Area of a Prism
- Right Prism
- Oblique Prism
- Rectangular Prism
- Volume of a Rectangular Prism
- Surface Area of a Rectangular Prism
- Triangular Prism
- Volume of a Triangular Prism
- Surface Area of a Triangular Prism
- Hexagonal Prism
- Volume of a Hexagonal Prism
- Surface Area of a Hexagonal Prism
- Pentagonal Prism
- Volume of a Pentagonal Prism
- Surface Area of a Pentagonal Prism
- Trapezoidal Prism
- Volume of a Trapezoidal Prism
- Surface Area of a Trapezoidal Prism
- Square Prism
- Volume of a Square Prism
- Surface Area of a Square Prism
- Octagonal Prism
- Heptagonal Prism
- Decagonal Prism

Last modified on August 3rd, 2023