Prism – Definition with Examples

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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
Triangular Prism
  • Cube
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
Regular Prism

  • Irregular 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

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

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.

Calculate the surface area and volume

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 cm2Volume = 1 2 bhl = 1 2 × 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
Right Prism

  • Oblique Prism
Oblique Prism

 Right PrismOblique Prism
 Right prismOblique Prism
HeightThe height is a lateral edge.Height is an altitude outside the prism.
Side facesSide faces are rectangles.Sides faces are parallelograms.
Surface Areabh+2ls+lbbh+2ls+lb
Volume1 2 bhl1 2 bhl
Fun Facts
– 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.



Prism – Definition with Examples

Shapes

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Prism – Definition with Examples

Angles

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Prism – Definition with Examples

Parallel and Perpendicular Lines

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