prism

Prism Definition

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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

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There are two major types of prisms. They are,

• Regular Prism
• Irregular Prism

There are many different types of prisms under these two prisms. 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.

Prism Images:

Irregular Prism:

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

Volume of Prism

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The space enclosed by a prism is called its volume. The volume of any prism is equal to the product of the base and the height.


Volume of prism = Area of base × Height of prism

Altitude of a Prism

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Altitude of a Prism can be defined as a line joining the two bases of the prism. The height of a Prism is also called as the altitude of a prism. It is also defined as the 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 starts from a base and ends in the second base of the prism.

→ Read More

Right Angle Prism

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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

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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. A square prism is simply 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 × 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 = s2 × h→ Read More

Prism Solved Examples

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Given below are some of the examples on prisms.

Solved Examples

Question 1: How to solve prism whose base area is 60 m² and the height is 30 m?
Solution:

Step 1: The given base area is 60 m² and height is 30 m
Step 2: The volume of the prism is, Volume = (Base area × Height) cubic units
Step 3: B = 60 m² and H = 30 m
Step 4: Volume = 60 × 30 = 1800
So, the volume of the prism is 1800 m³

Question 2: If the volume of the triangular prism is 350 cm³ 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 cm³
Volume of Prism = 12 * a * b * h = A h
Therefore, the altitude of the triangular prism, a = 2×Volumeb×h
= 2×35012×10
= 700120
= 5.8

Therefore, the altitude of the triangular base is 5.8 cm

Question 3: If the volume of the triangular prism is 500 cm³ 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 cm³
Volume of Prism = 12 * a * b * h = A h
Therefore the altitude of the triangular prism, a = 2×Volumeb×h
= 2×50016×20
= 1000320
= 3.125
Therefore, the altitude of the triangular prism is 3.125 cm.

Prism Definition

Back to Top

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

Back to Top

There are two major types of prisms. They are,

• Regular Prism
• Irregular Prism

There are many different types of prisms under these two prisms. 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.

Prism Images:

Irregular Prism:

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

Volume of Prism

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The space enclosed by a prism is called its volume. The volume of any prism is equal to the product of the base and the height.


Volume of prism = Area of base × Height of prism

Altitude of a Prism

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Altitude of a Prism can be defined as a line joining the two bases of the prism. The height of a Prism is also called as the altitude of a prism. It is also defined as the 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 starts from a base and ends in the second base of the prism.

→ Read More

Right Angle Prism

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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

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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. A square prism is simply 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 × 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 = s2 × h→ Read More

Prism Solved Examples

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Given below are some of the examples on prisms.

Solved Examples

Question 1: How to solve prism whose base area is 60 m² and the height is 30 m?
Solution:

Step 1: The given base area is 60 m² and height is 30 m
Step 2: The volume of the prism is, Volume = (Base area × Height) cubic units
Step 3: B = 60 m² and H = 30 m
Step 4: Volume = 60 × 30 = 1800
So, the volume of the prism is 1800 m³

Question 2: If the volume of the triangular prism is 350 cm³ 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 cm³
Volume of Prism = 12 * a * b * h = A h
Therefore, the altitude of the triangular prism, a = 2×Volumeb×h
= 2×35012×10
= 700120
= 5.8

Therefore, the altitude of the triangular base is 5.8 cm

Question 3: If the volume of the triangular prism is 500 cm³ 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 cm³
Volume of Prism = 12 * a * b * h = A h
Therefore the altitude of the triangular prism, a = 2×Volumeb×h
= 2×50016×20
= 1000320
= 3.125
Therefore, the altitude of the triangular prism is 3.125 cm.