Prism

Prism

A prism is a solid geometric figure with two parallel, flat surfaces connected by rectangular faces. The bases can be any polygon (triangular, rectangular, pentagonal, etc.), and the cross-section along the length of the prism remains the same.

1. Base of a Prism

The base of a prism refers to one of the two parallel, congruent faces of the prism. These bases determine the shape and type of the prism (e.g., if the base is a triangle, it’s a triangular prism).

2. Height of a Prism

The height of a prism is the perpendicular distance between its two bases. It represents the depth or length of the prism.

3. Cross-section of a Prism

The cross-section of a prism is the shape obtained when you make a straight cut parallel to the bases. The cross-sectional area remains constant throughout the length of the prism.

Surface Areas and Volume of a Prism

1. Lateral Surface Area (LSA) of a Prism

The Lateral Surface Area of a prism is the area of the faces excluding the two bases. It is the total area of all rectangular faces connecting the bases.

Formula: 

\(\text{LSA} = \text{Perimeter of Base} \times \text{Height}\)

2. Total Surface Area (TSA) of a Prism

The Total Surface Area of a prism is the sum of the areas of all its faces, including both bases and the lateral faces.

Formula: 

\(\text{TSA} = \text{LSA} + 2 \times \text{Area of Base}\)

or

\(\text{TSA} = (\text{Perimeter of Base} \times \text{Height}) + 2 \times\text{Area of Base}\)

Volume of a Prism

The volume of a prism is the amount of space enclosed within it.

Formula: 

\(\text{Volume} = \text{Area of Base} \times \text{Height}\)

Summary

1. LSA tells us only about the side faces.

2. TSA includes all faces (side faces + bases).

3. Volume tells us how much space is inside the prism.