Table of Contents

Last modified on March 28th, 2023

A prism is a three-dimensional soild object having two identical and parallel shapes facing each other. The identical shapes are called the bases. The bases can have any shape of a polygon such as triangles, square, rectangle, or a pentagon. The diagram below shows a triangular prism.

A prism is a member of the polyhedron family consisting of two identical and parallel polygonal bases. The bases are connected by flat faces forming a uniform cross-section.

In general, a prism refers to a transparent solid used to refract or scatter a beam of white light. It is a commonly used instrument in physics.

A prism has bases, lateral faces, edges, and vertices.

**Base**– The**parallel faces**which makes the 2 ends of any prism. They are congruent. The base determines the cross-section of any prism and it remains uniform throughout the shape.**Lateral faces**– The**non-parallel faces**which connects the 2 bases.**Vertices**– The corners.**Edges**– Where any 2 faces meet.

Depending on the base, a prism can be of different shapes. Some common shapes are: triangular, rectangular, square, pentagonal, hexagonal, heptagonal, octagonal, and trapezoidal. For example, a triangular prism has a triangular base and a square prism has a square base, here are some more shapes:

A prism can also be classified into **regular** or **irregular** based on the uniformity of its cross-section. It can be **right** or **oblique**, depending on the alignment of its bases.

The diagram shows the difference between a regular and irregular triangular prism.

**Regular Prism**– It has a base which is a regular polygon with equal side lengths. Regular prisms have identical bases and identical lateral faces. Thus, all the above examples of prisms are regular such as triangular, rectangular, and pentagonal.**Irregular Prism**– It has a base which is an irregular polygon with unequal side lengths. Irregular prisms have identical bases. However, the lateral faces are not identical.

The diagram shows the difference between a right and an oblique pentagonal prism.

**Right Prism –**Its lateral faces are perpendicular to its bases. The 2 bases of a right prism is aligned perfectly over one another.**Oblique Prism**– It is a slanted prism. So its lateral faces are not perpendicular to its bases. The 2 bases are not aligned perfectly over one another.

Like all other polyhedrons, a prism also has a surface area and a volume.

**Lateral Surface Area (LSA) = Perimeter × Height**

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

∴**TSA= (2 × Base Area) + (Perimeter × Height)**

here, height is the distance between the 2 bases or the length of the prism.

**Volume = Base Area × Height**, here, height is the distance between the 2 bases or the length of the prism.

Let us solve some examples involving prisms and the above formulas

**Find the surface area of a triangular prism given whose base area is 12 cm ^{2}, perimeter is 16 cm, and length is 7 cm.**

Solution:

As we know,**Total Surface Area (TSA) = (2 × Base Area) + (Perimeter × Height),** here base Area = 12 cm^{2}, perimeter = 16 cm, height = length = 7 cm

∴ TSA = (2 × 12) + (16 × 7)

= 136 in^{2}

**Find the total and lateral surface area of a rectangular prism whose base area is 36 cm ^{2} , perimeter is 30 cm, and height is 11 cm.**

Solution:

As we know,**Total Surface Area (TSA) = (2 × Base Area) + (Perimeter × Height)**, here base area = 36 cm^{2}, perimeter = 30 cm, height = 11 cm

∴ TSA = (2 × 36) + (30 × 11)

= 402 cm^{2}**Lateral Surface Area (LSA) = Perimeter × Height**

∴ LSA = 30 × 11

= 330 cm^{2}

**Find the** **volume of a triangular prism whose base area is 64 cm ^{2} and height is 7 cm.**

Solution:

As we know,

Volume (V) = Base Area × Height

∴ V= B × h, here B = 64 cm^{2}, h = 7 cm

= 64 × 7

= 448 cm^{3}

- Ice cubes and candy bars
- Books and notebooks
- A Rubik’s cube
- Camping tents and barns
- Glass or plastic prisms used in science laboratories to see spectrum of white light

**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 March 28th, 2023

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