[Maths Class Notes] on Prism Pdf for Exam

A prism features a very solid shape that consists of two identical ends (like triangle, square, rectangle, etc.), the flat faces or the surfaces, and the uniform cross-section across its length. The cross-section looks like a triangle hence called triangular prisms. The shape of a prism doesn’t have any curve. So, a prism can also have a square, a rectangular, a pentagonal, and many other polygon shapes but not a circular shape.

Cross Section of Prism

The cross-section is the point where the shape obtained by the intersection of an object by a plane along its axis. It is also said as cutting a three-dimensional object with a plane to get another shape.

If a prism is intersected by a plane, parallel to the base, then the shape of the cross-section will be the same as the base. For instance, a square pyramid is cut by a plane, parallel to the base, then the shape of the cross-section of the pyramid will also be a square.

Types of Prism

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

• Regular Prism

• Irregular Prism

Regular Prism

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

Irregular Prism

If the base of a prism is within the shape of an irregular polygon, then the prism is called an irregular prism.

Prism Based on Shape of Bases

Based on the shape of the bases, it is further categorized into different types, namely;

• Triangular prism (has triangular bases).

• Square prism (has square bases).

• Rectangular prism (has rectangular bases).

• Pentagonal prism (has pentagonal bases).

• Hexagonal prism (has hexagonal bases).

Right Prism and Oblique Prism

Apart from regular and irregular, the prism is often classified into two more types;

The difference between both the prism for triangular bases are given below;

Difference Between Right and Oblique Prism

Properties of Prism

1. A prism may be a sort of three-dimensional (3D) shape with flat sides.

2. It has two ends that are an equivalent shape and size (and appear as if a 2D shape).

3. It has an equivalent cross-section right along with the form from end to end; meaning if you narrow through it you’d see an equivalent 2D shape as on either end.

Formulas (Surface Area & Volume)

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

Volume of a Prism

The volume of the prism is defined because of the product of the bottom area and therefore the prism height.

Therefore,

For example, if you want to find the volume of a square prism, then it is important to know the area of a square, then its volume can be calculated as follows:

The volume of the square Prism equals the Area for square × height.

V = s² × h cubic units

Where “s” is the side of a square.

Surface Area of a Prism

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

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

Solved Problems

Example 1: Find the volume of a given triangular prism whose area is given to be 60 cm2 and given height is 7 cm.

Solution: Given,

Base area = 60 cm2

Height = 7 cm

We know that,

The volume for the prism equals (Base area × Height) cubic units

Therefore, V = 60 × 7 = 420

Hence, the volume of a triangular prism = 420 cm3.

Example 2: Find the height of the square prism whose volume is equal to 360 cm³ and the base area is 60 cm².

Solution: Given,

The volume for the square prism = 360 cm3

Base Area = 60 cm2

So, the height for the square prism is calculated as given below:

The volume for the square prism equals the Base area × height

360 = 60 × prism height

Therefore, the height, h = 360/60

Prism Height, h = 6 cm.