What is Prism

A prism is a 3dimensional shape with two identical shapes facing each other. These identical shapes are called “bases”.

The bases can be a triangle, square, rectangle or any other polygon.

Other faces of a prism are parallelograms or rectangles.
Cross Section of Prisms
The cross section of a geometric shape or an object is the shape obtained by cutting it straight. It is also referred to as the intersection of a plane with the threedimensional object. The cross section of a prism parallel to the base of the prism is same as its base.
 Triangular Prism
 Cube
Regular and Irregular Prism
The base of a prism can be a regular or irregular polygon. Based on the shape of the base, prisms are regular or irregular prisms.
 Regular Prism
 Irregular Prism
Surface Area and Volume of a Prism
The surface area of a prism is the sum of the area of all its faces.
Volume of a prism is the amount of space inside the prism.
Let us see how to find the surface area and volume of a triangular prism.
 Surface Area
Surface Area = Area of base triangles + Area of side parallelograms
= 2 × ( 1 2 x b x h) + 2 × (l x s) + (l x b)
= bh + 2ls + lb
 Volume
Volume = Area of base triangle × length
= ( 1 2 b x h) × l
= 1 2 bhl
Example: Calculate the surface area and volume of the following prism.
Length (l) = 12 cm, Height (h) = 4 cm, Base (b) = 6 cm, Side (s) = 5 cm
Surface area = bh+2ls+lb = 6 × 4 + 2 × 12 × 5 + 12 × 6 = 24 + 120 + 72 = 216 cm^{2} 
Volume = 1 2 bhl = 1 2 × 6 × 4 × 12 = 144 cm^{3} 
Right Prism and Oblique Prism
When the two bases of a prism are perfectly aligned and its faces are rectangles (perpendicular to the bases) it is a right prism, else it is an oblique. They are characterized as follows:
 Right Prism
 Oblique Prism
Right Prism 
Oblique Prism 

Height 
The height is a lateral edge. 
Height is an altitude outside the prism. 
Side faces 
Side faces are rectangles. 
Sides faces are parallelograms. 
Surface Area 
bh+2ls+lb 
bh+2ls+lb 
Volume 
1 2 bhl 
1 2 bhl 
Fun Facts
