Table of Contents

Last modified on August 3rd, 2023

A square prism is a three-dimensional solid consisting of two identical square bases joined together by four rectangular faces. It has 6 faces (2 square and 4 rectangular), 12 edges, and 8 vertices.

Toothpaste packs, eye drops or liquid medicine packs, and bar magnets are some common examples of square prisms we see in our daily life.

A 2-dimensional net can be used to construct a square prism to understand its shape. Generally a net is made from paper and cut in a manner such that it can be folded and modified into 3-D shape.

A square prism can be **right** or **oblique** depending on the alignment of its bases.

A right square prism is a prism in which the lateral faces are perpendicular to its bases. Thus, the lateral faces are rectangular. Therefore, the bases are aligned perfectly above one another when the prism rests on its base.

An oblique square prism is a slanted prism in which the lateral faces are not perpendicular to its bases. Thus, the lateral faces are parallelogram-shaped. Therefore, the bases do not appear above one another when the prism rests on its base.

The formula to calculate the total surface area is given below:

**Total Surface Area (****TSA****) = ****2 a^{2} + 4al**, here

Also**, **since **Lateral Surface Area (*** LSA)* = Base perimeter

Here, Base Perimeter = 5 ⨯ base edge ⨯ length = **4 al**

∴**Lateral Surface Area (*** LSA)* =

Thus, we can write

**Total Surface Area (****TSA****) = 2 a^{2} + **

Let us solve some examples to understand the concept better.

**Find the lateral and the total surface area and volume of a square prism with a square face of base edge 6 in and length 9 in.**

Solution:

As we know,

Lateral Surface Area (*LSA)* = 4*al, *here *a* = 6 in, *l* = 9 in

∴ *LSA* = 4 × 6 × 9

= 216 in^{2}

Total Surface Area (*TSA*) = 2*a ^{2} *+

∴

= 288 in

**Find the lateral surface area of a square prism given in the figure.**

Solution:

As we know,

Lateral Surface Area (*LSA*) = 4*al*, here *a* = 3 ft, *l* = 7.6 ft

∴ *LSA* = 4 × 3 × 7.6

= 91.2 ft^{2}

The volume of a square prism is its space in the three-dimensional plane. The formula is given below:

**Volume (V) = a^{2}l, **here

Let us solve an example to understand the concept better.

**Find the volume of a square prism with a base edge of 7 cm and length of 11 cm.**

Solution:

As we know,

Volume* (V) = a ^{2}l, *here

∴

= 539 cm

**More Resources:**- Volume of a Prism
- Surface Area of a Prism
- Right Prism
- Oblique Prism
- Rectangular Prism
- Volume of a Rectangular Prism
- Surface Area of a Rectangular Prism
- Triangular Prism
- Volume of a Triangular Prism
- Surface Area of a Triangular Prism
- Hexagonal Prism
- Volume of a Hexagonal Prism
- Surface Area of a Hexagonal Prism
- Pentagonal Prism
- Volume of a Pentagonal Prism
- Surface Area of a Pentagonal Prism
- Trapezoidal Prism
- Volume of a Trapezoidal Prism
- Surface Area of a Trapezoidal Prism
- Square Prism
- Volume of a Square Prism
- Surface Area of a Square Prism
- Octagonal Prism
- Heptagonal Prism
- Decagonal Prism

Last modified on August 3rd, 2023