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# Prism

Prisms are solids whose two ends are exactly the same shape. It is named after the shape of the faces at each end. Prisms are the combination of flat faces, identical ends (bases) and same cross section, as we can see in below figure. Faces and the combination ends are at right angles to the base faces of the prism.

### Prism Shape:

 Related Calculators Prism Calculator Calculate Volume of a Triangular Prism Calculate Volume of Rectangular Prism Prism Surface Area Calculator

## Prism Definition

Prism is a three-dimensional shape which has two parallel end faces. These end faces are of same shape and size, and each of whose sides is a parallelogram. If we take any cross section of a prism parallel to the bases, the cross section will look just like the bases.

## Types of Prism

Mainly we discussed about two major types of prisms:

• Regular Prism
• Irregular Prism

Below you can see prisms and their corresponding cross sections. Here cross section is the same all along its length.

### Regular Prism:

A prism with regular polygon bases is called as regular prism. The height of a regular prism is the distance between the bases.

### Irregular Prism:

The bases of irregular prisms are irregular polygons and the faces are not equally sized.

## Volume of Prism

The volume of any prism is equal to the product of the base and its height.

Volume of prism = Area of base $\times$ Height of prism

## Altitude of a Prism

Altitude of a Prism is a line joining the two bases of the prism. The height of a Prism is also called as the altitude or shortest distance between the two bases of a prism.

In the figure shown above, we can see the altitude of the prism.
Altitude of a Prism can also be defined as a perpendicular segment that joins two bases of the figure.

## Right Angle Prism

A prism is a three dimensional solid with two congruent, parallel, polygonal bases. A right prism is a prism whose faces are perpendicular to the prism's bases.

## Square Prism

A prism whose end faces are squares is a square prism. When we take cross section of a square prism parallel to its bases, we get a square. Also called as a cuboid with square bases. A square prism which has square lateral surfaces is a cube.

The bases of a square prism are squares.
Volume of any prism = Area of base $\times$ height

Since base of the prism is square, so the area of base = (side)$^2$

If each side of square base is 's' and height of the prism is 'h', then we have

Volume of square prism = s$^2$ $\times$ h

## Prism Solved Examples

Given below are some of the examples.
Example 1:

How to solve prism whose base area is $60 m^2$ and the height is $30 m$?

Solution:

Step 1: The given base area is $60 m^2$ and height is $30 m$

Step 2: The volume of the prism is, Volume = $(Base\ Area\ \times\ Height)$ cubic units

Step 3: $B$ = $60 m^2$ and $H$ = $30 m$

Step 4: Volume = $60\ \times\ 30$ = $180^{\circ}$

So, the volume of the prism is $180^{\circ}\ m^3$
Example 2:

If the volume of the triangular prism is $350 cm^3$ and base is $12 cm$, height is $10 cm$, then find the altitude of the triangular base.

Solution:

The base of a triangular prism = $12 cm$

The height of a triangular prism = $10 cm$

The volume of a triangular prism = $350 cm^3$

Volume of Prism = $\frac{1}{2}$ $\times\ a\ \times\ b\ \times\ h$ = $A h$

Therefore, the altitude of the triangular prism,

$a$ = $\frac{2 \times \text{Volume}}{b \times h}$

= $\frac{2 \times 350}{12 \times 10}$

= $\frac{700}{120}$

= $5.8$

Therefore, the altitude of the triangular base is $5.8 cm$

Example 3:

If the volume of the triangular prism is $500 cm^3$ and base is $16 cm$, height is $20 cm$ then find the altitude of the triangular base.

Solution:

The base of a triangular prism = $16 cm$

The height of a triangular prism = $20 cm$

The volume of a triangular prism = $500 cm^3$

Volume of Prism = $\frac{1}{2}$ $\times\ a\ \times\ b\ \times h$ = $A h$

Therefore the altitude of the triangular prism,

$a$ = $\frac{2 \times \text{Volume}}{b \times h}$

= $\frac{2 \times 500}{16 \times 20}$

= $\frac{1000}{320}$

= $3.125$

Therefore, the altitude of the triangular prism is $3.125 cm$.

 More topics in Prism Surface Area of a Prism Volume of a Prism Square Prism Triangular Prism Rectangular Prism Altitude of a Prism Circular Prism
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