Square Prism

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Square Based Prism

As per the square prism definition, it is a three-dimensional geometric solid object that has a base of a square. In a square prism, the sides and angles opposite of each other are congruent. Thus, when a minimum of two of the sides and angles are equal in measurement, it can also be termed as a square prism. You can also consider cuboid whose base is square as a square prism. In the illustration below, you can see that the bases are squared and thus it is a square prism.


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The Volume of a Square Prism

The volume of a square-based prism is a computation of the inhabited units of the solid. The volume of a square prism is the number of units that are used to fill a cube. It is represented in the form of cubic units.

We have the formula to calculate the volume of a square prism, i.e. V= a²h cubic units

Where,

V = volume

A = side of the base

H = height of the prism


How to Calculate Surface Area of a Square Prism

The surface area of a square prism is a quantification of the total area of a surface of a 3-D solid object. For a square-based prism, the surface area is defined as the sum total of twice the base area and the lateral surface area (LSA) of the prism. Its measure is represented in square units.

Formula to find the surface area of a square prism is as follows:

The surface area of the square prism i.e. SA = 2a² + 4ah square units

In which,

a = side of the square prism

h = height of the square prism


Is Square Prism a Cube?

A cube is a unique case of a square prism where the lengths in all the three dimensions are identical. Hence, all cubes make square prisms but not all square prisms are cubes.


Types of Prisms

There are different prisms that are categorized based on the cross-section. These are as given:

  • Square Prism

  • Rectangular Prism

  • Triangular Prism

  • Oblique Prism

  • Cubical Prism

  • Pentagonal Prism

Note: prism with rectangular base is also sometimes called a square prism.


Cross Section in a Prism

A cross section is a shape obtained by cutting straight through an object.

For example, in the image below, the cross-section of the object is a triangle and also contains  Identical cross-section all along its length, therefore it is a triangular prism.


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Solved Examples on Prisms

Example:

Find the surface area of a prism where the base area is 20 m², the base perimeter is 22 m, and the length is 10 m.

Solution:

Surface Area of A Prism = 2 × (Base Area + Base Perimeter) × Length

 Thus, we get

= 2 × 20 m² + 22 m × 10 m

= 40 m² + 220 m²

= 260 m²


Example:

Calculate the volume and the surface area of a square prism whose side is 7 cm and height is 11 cm.

Solution:

Given:

Side, a = 7 cm

Height, h = 11 cm

The Volume a Square Prism, V = a² h cubic units.

V = (7)² (11)

V = 49 (11)

V = 539 cm³

Hence, the volume of a square prism is 539 cm³

The surface area of the square prism, SA = 2a² + 4ah square units

Substituting the given values, we get

SA = 2(7)² + 4(7)(11) cm²

SA = 2(49) + 4(77) cm²

SA = 98 + 308 cm²

SA = 406 cm²

Thus, the surface area of a given square prism is 406 cm².

FAQ (Frequently Asked Questions)

Q1. Why do we Call a Prism a Square Prism?

Answer: As there are a variety of shapes that can serve as the base of a prism, there are different forms of prisms that can be created. Prisms are basically named for the shape of their bases, so a square prism attained its name due to the squares in its bases.

Q2. What is an Example of a Square Prism?

Answer: Think about the rolling dice. You will get a clear idea of how a square prism is. Dice is an enclosed 3-dimensional shape, which is based on two squares. For a fact, regular dice are cubed; all the faces of this solid object are square. So cubes are actually a square prism regardless of how they are looked at! Another common real-world example is the famous Rubik's Cube. Also, imagine diced cubes of cottage cheese, those are square prisms too.

Q3. How can we Spot a Square Prism Easily?

Answer: When finding out a square prism, make sure that you do not have to look for all the faces that are squares. As long as the solid object has two square faces, meaning its bases are squares, it's a square prism.

Q4. What are the Properties of a Prism?

Answer: A prism is a solid 3-dimensional figure with:

  • Flat faces.

  • Uniform and similar ends.

  • Same cross-section all along its length!