Rectangular Prism (original) (raw)

Last Updated : 23 Jul, 2025

**Rectangular Prism in mathematics is a three-dimensional geometric figure with four lateral faces and two parallel faces. A rectangular prism is one whose two parallel bases are rectangular. A rectangular prism is observed by us in our daily life such as boxes, almirahs, etc. all resembling a rectangular prism.

This guide explores the **rectangular prism formula for volume and surface area and illustrates the typical **rectangular prism shape encountered in everyday life.

What is a Rectangular Prism?

A rectangular prism in geometry is a polyhedron. It is a 3-D figure which has parallel bases. A rectangular prism is similar to a cuboid and has a total of six faces. There are three pairs of identical faces in a rectangular prism. The top and bottom faces of a rectangular prism are called the bases of the rectangular prism. The image added below shows a rectangular prism.

Rectangular-Prism

Net of a Rectangular Prism

Net of a figure is the 2-D representation of the figure. Suppose we take a 3-D figure made of carbord and open it then the figure so obtained is called the net of 3-D figure.

The image showing net of a rectangular prism is added below,

Rectangular-Prism-Net

Faces Edges Vertices of a Rectangular Prism

In a rectangular prism we have 6 faces, 12 edges (sides) and 8 vertices. A rectangular prism is also called a cuboid and three sides of a rectangular prism intersect at right angles.

Table of Content

Types of Rectangular Prism

Rectangular prism are categorised into two categories based on their shapes that are,

**Right Rectangular Prism

A right rectangular prism is rectangular prism in which the base and top of rectangular prism are connected using right faces, i.e. they are connected using faces at right angle.

**Oblique Rectangular Prism

A oblique rectangular prism is rectangular prism in which the base and top of rectangular prism are connected using faces, that are not connected using right faces, but are connected using Oblique faces.

The image added below shows the Right Recatngular Prism and Oblique Recatngular Prism

Right and Oblique Rectangular-Prism

Properties of Rectangular Prism

Various properties of rectangular prism are added below,

Rectangular Prism Formulas

Various formulas related to the rectanular prims are,

Let's learn about them in detail.

**Surface Area of Rectangular Prism

The surface area of a rectangular prism is equal to the total sum of the surface areas of all its faces. A rectangular prism has two types of surface areas that are,

Let's learn about them in detail.

Lateral Surface Area of Rectangular Prism

A rectangular prism's lateral surface area can be found by calculating the sum of the areas of its four lateral faces, i.e., the total area of the prism excluding the areas of its two bases.

The **lateral surface area formula of rectangular prism is given as,

**LSA of Rectangular Prism = 2h (l + b) square units

where,

Total Surface Area of Rectangular Prism

The total surface area of a rectangular prism is equal to the total sum of the surface areas of all its faces. Now, since it is composed of all rectangular faces, and the area of a rectangle is given by the product of its length and width, add up all the products of lengths and breadths to conjure up the surface area of a rectangular prism.

The **total surface area formula of rectangular prism is given as,

**TSA of Rectangular Prism = 2(lb + lh + bh)

where,

Volume of Rectangular Prism

Volume of a rectangular prism is the total space occupied by the rectangular prism. The volume of rectangular prism is calculated using length, breadth, height of the rectangular prism, it unit is cubic unit, or unit3

**Volume of Rectangular Prism(V) = l.b.h

where,

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**Solved Examples on Rectangular Prism

**Example 1: Find the surface area of a rectangular prism if its length, breadth, and height are 4 m, 5 m, and 8 m.

**Solution:

Given,

SA = 2(lb + lh + bh)

= 2(4 × 5 + 4 × 8 + 5 × 8)

= 2(20 + 32 + 40)

= 2(92)

**A = 184 m 2

**Example 2: Find the surface area of a rectangular prism if its length, breadth, and height are 2 m, 7 m, and 10 m.

**Solution:

Given,

SA = 2(lb + lh + bh)

= 2(2 × 7 + 2 × 10 + 7 × 10)

= 2(14 + 20 + 70)

= 2(104)

**A = 208 m 2

**Example 3: Find the surface area of a rectangular prism if its length, breadth, and height are 9 m, 6 m, and 7 m.

**Solution:

Given,

SA = 2(lb + lh + bh)

= 2(9 × 6 + 7 × 9 + 6 × 7)

= 2(54 + 63 + 42)

= 2(159)

**A = 318 m 2

**Example 4: Find the lateral surface area of a rectangular prism if its length, breadth, and height are 21 cm, 15 cm, and 18 cm.

**Solution:

Given,

LSA = 2h (l+ b)

= 2 × 18 (21 +15)

= 36 × 36

**LSA = 1,296 cm 2

**Example 5: Find the volume of a rectangular prism if its length, breadth, and height are 7 m, 6 m, and 5 m.

**Solution:

Given,

Volume of Rectangular Prism(V) = l.b.h

V = 7.6.5

V = 210 m3

The volume of rectangular prism is 210 m3

**Example 6: Find the lateral surface area of a rectangular prism if its length, breadth, and height are 15 cm, 10 cm, and 13 cm.

**Solution:

Given,

LSA = 2h (l+ b)

= 2 × 13 (15 + 10)

= 26 × 25

**LSA = 650 cm 2

**Example 7: Find the volume of a rectangular prism if its length, breadth, and height are 8 m, 5 m, and 9 m.

**Solution:

Given,

Volume of Rectangular Prism(V) = l.b.h

V = 8.5.9

V = 360 m3

The volume of rectangular prism is 360 m3

Practice Questions on Rectangular Prism

**Q1: What is the volume of a rectangular prism with length 4 cm, width 7 cm and height 9 cm?

**Q2: Find the Surface Area of a Rectangular Prism with length 3 cm, breadth 5 cm and height 6 cm.

**Q3: What is the Surface Area of a Rectangular Prism with length 9 cm, width 12 cm and height 6 cm?

**Q4: Find the volume of a Rectangular Prism with length 5.5 cm, width 4.5 cm and height 3.5 cm