Prism - Definition with Examples

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Prism Games

Volume of solids
Volume of Solids

Find the volume of solids by multiplying the area of the base by the height of the solid. Remember, that volume like area can be added.

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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 cm2

Volume = 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 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

  • 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.

 

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