What is a prism ?.

What is Prism

• A prism is a 3-dimensional 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 three-dimensional 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 × (12 x b x h) + 2 × (l x s) + (l x b) 

= bh + 2ls + lb

• Volume

Volume = Area of base triangle × length

= (12 b x h) × l

=12 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 cm2

Volume = 12 bhl =12 × 6 × 4 × 12 = 144 cm3

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	12 bhl	12 bhl

The prisms are polyhedrons or objects with multiple flat faces. A prism can not have any side which is curved thus objects like cylinder, cone or sphere are not prisms.