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Prismis a three-dimensional solid object in which the two ends are exactly of the same shape. It is the combination of the flat faces, identical bases and same cross-sections. The faces are parallelograms without the bases. If you take the cross-section of the prism parallel to the bases, the cross-sections will look like the bases. In this article, let us have a complete explanation about the types and also how to find the volume and area of a prism.## Prism Shape

A prism has a solid shape consisting of two equal ends, flat faces or surfaces and identical cross-section across its length. The cross-section looks like a triangle hence called triangular prism. The shape of the prism does not have any curve. Hence, a prism can have cubic, rectangular, pentagonal and other polygon shapes but not the circular shape.

## Types of Prism

Depending upon the cross-sections, the prisms are named. It is of two types, namely;

## Regular Prism

If the bases of the prism are in the shape of a regular polygon, it is called regular prism.

## Irregular Prism

If the bases are in the shape of an irregular polygon, then the prism is called an irregular prism.

## Right Prism And Oblique Prism

Apart from regular and irregular, the prism can be classified into two more types;

The difference between both the prism are;

Right PrismOblique PrismBased on the shape of the bases, it is further categorised into different types, namely;

## Prism Formulas

The formulas are defined for the surface area and volume of the prism. As the prism is a three-dimensional shape, so it has both the properties, i.e., surface area and volume.

## Surface Area of a Prism

The surface area of the prism is the total area covered by the faces of the prism.

For any kind of prism, the surface area can be found using the formula;

Surface Area of a Prism = 2(Base Area)+ (Base perimeter × length)## Volume of a Prism

The volume of the prism is defined as the product of the base area and the prism height

Therefore,

Volume of Prism = Base Area × HeightFor example, if you want to find the volume of a square prism, you must know the area of a square, then its volume can be calculated as follows:

The volume of a square Prism = Area of square×height

V = s

^{2}× h cubic unitsWhere “s” is the side of a square.

## Prism Problems

Example 1: Find the volume of a triangular prism whose area is 60cm^{2}and height is 7cm?Solution:Given,Area = 60 cm

^{2}Height = 7 cm

We know that,

The volume of a prism = Base area × Height cubic units

Therefore, V = 60 ×7 = 420

Hence, the volume of a triangular prism = 420 cm

^{3}.Example 2: Find the height of the square prism whose volume is 360 cm^{3}and the base area is 60 cm^{2}?Solution:Given,The volume of a square prism = 360cm

^{3}Base Area = 60cm

^{2}Therefore, the height of the square prism is calculated as follows:

The volume of square prism = Base area × height

360 = 60 × prism height

Therefore, the height,h = 360/60

Prism Height, h = 6 cm.

A VIDEO ABOUT VOLUME OF DIFFERENT OBJECTS## ASSIGNMENT : VOLUME ASSIGNMENT

MARKS : 30 DURATION : 2 hours

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