A three-dimensional solid shape having its base and top as identical polygons and side faces as parallelograms are called a prism.

A Prism is a Solid Object with:

Identical base and top which are parallel to each other.

The side faces are flat and parallelogram

No curve sides

And the same cross-section along with its length.

A prism is a solid three-dimensional geometric figure with two similar ends and all flat sides. The prism is named after the shape of its base, hence a prism with a triangular base is called a "triangular prism”. So the different types of prisms are given their names on the basis of their cross-sectional figure formed.

Types of Prisms are:

Triangular Prism

Square Prism

Cube

Cuboid or rectangular Prism

Pentagonal Prism

As the prism is a 3D solid object it has both the surface area and volume.

The volume of a 3D prism is defined as the total space occupied by that object.

To calculate the volume of a prism, you just have to calculate the area of its base and multiply it by its height.

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The volume of a three-dimensional prism is represented as cubic units.

Here's how to calculate the volume of a variety of prisms.

Different prisms have different volumes. So the formula to calculate the volume of different Prisms are:

Triangular Prism

A prism having its base and top as identical triangles and the lateral faces are rectangles is called a triangular prism.

A triangular prism has

5 faces

6 vertices and

9 edges

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Where,

a = Apothem length of a triangular prism

b = Base length of a triangular prism

h = height of a triangular prism

Square Prism

In a square prism, the base and top are congruent squares and the lateral faces are rectangles

A square prism has

6 faces

8 vertices and

12 edges

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Where

l = length of a square prism

b = Base of a square prism

h = height of a square prism

Cube

If a square prism has all of its faces as identical squares, then it is called a cube prism.

A cubic prism or a cube has

6 faces

8 vertices and

12 edges

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Where

a = edges of a cube prism( because l = w = h = a)

Cuboid or Rectangular Prism

If the base and top of the prism are identical rectangles, then it is a rectangular prism or a cuboid.

A cuboid prism has

6 faces

8 vertices and

12 edges

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Where

l = length of a rectangular prism

b = Base of a rectangular prism

h = height of a rectangular prism

Pentagonal Prism

If the base and top of a prism are pentagons, then it is called a pentagonal prism.

A pentagonal prism has

7 faces

10 vertices and

15 edges

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Where,

a – Apothem length of the pentagonal prism.

b – Base length of the pentagonal prism.

h – Height of the pentagonal prism

Hexagonal Prism

A hexagonal prism is a prism with six rectangular faces and top and base as hexagonal.

A hexagonal prism has

8 faces

12 vertices and

18 edges

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Where

a – Apothem length of the hexagonal prism.

b – Base length of the hexagonal prism.

h – Height of the hexagonal prism.

Example 1 : Find the volume of the triangular prism given below.

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Solution:

Given that a = Apothem length of a triangular prism = 9cm

b = Base length of a triangular prism = 12 cm

h = height of a triangular prism = 18cm

We have, Volume of triangular prism = (\[\frac{1}{2}\]) a x b x h

= \[\frac{1}{2}\] x 9 x 12 x 18

= 972 \[cm^{3}\]

So the volume of the triangular prism is 972 cubic centimeter.

Example 2: Find the volume of rectangular prism given below.

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Solution:

Given that: l = length of a rectangular prism = 9cm

b = Base of a rectangular prism = 7cm

h = height of a rectangular prism = 13cm

We have, Volume of Rectangular Prism = l x b x h

= 9 x 7 x 13

= 819 \[cm^{3}\]

Therefore the volume of rectangular prism is 819 cubic centimeters.

Find the volume for the triangular prism given below

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FAQ (Frequently Asked Questions)

1. What is a Polygon?

Answer: A two-dimensional closed figure bounded with three or more than three straight lines is called a polygon. Triangles, square, rectangle, pentagon, hexagon, are some examples of polygons.

The below figures show some of the examples of polygons.

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In figure 1 you can see that all the shapes are polygons, as all the shapes are drawn joining the straight lines only. There are no curved lines. Even the shape in orange color is a polygon because it is formed by joining straight lines and it is a closed figure.

But in figure 2 the shape is not a polygon because it is not fully connected and also has curved lines.

The name of the polygon itself implies the number of sides in it. For instance, a triangle is a polygon having three sides, a quadrilateral is a polygon having four sides, etc.

2. What is Pyramid?

Answer: A solid shape having its base as any polygon and side face as triangles with a common vertex is called a pyramid.

The most commonly used pyramid is the square pyramid i.e., it has a square base and four triangular side faces.

Some of the properties of a square pyramid are :

A square pyramid has 5 vertices, 8 edges, and 5 faces

(image will be uploaded soon)Volume of Prism Formula