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.
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,
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
- Oblique Rectangular Prism
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
Properties of Rectangular Prism
Various properties of rectangular prism are added below,
- A rectangular prism has 6 Faces, 8 Vertices, and 12 Edges.
- A rectangular prism has three dimension that are, Length, Width, and Height
- A rectangular prism has 3 pair of identical faces, etc.
Rectangular Prism Formulas
Various formulas related to the rectanular prims are,
- Surface Area of a Rectanular Prism
- Volume of Rectangular Prism
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,
- Lateral Surface Area
- Total Surface Area
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,
- l is Length of Rectangular Prism
- b is Breadth of Rectangular Prism
- h is Height of Rectangular Prism
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,
- l is Length of Rectangular Prism
- b is Breadth of Rectangular Prism
- h is Height of Rectangular Prism
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,
- l is Length of Rectangular Prism
- b is Breadth of Rectangular Prism
- h is Height of Rectangular Prism
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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,
- l = 4 m
- b = 5 m
- h = 8 m
SA = 2(lb + lh + bh)
= 2(4 × 5 + 4 × 8 + 5 × 8)
= 2(20 + 32 + 40)
= 2(92)
A = 184 m2
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,
- l = 2 m
- b = 7 m
- h = 10 m
SA = 2(lb + lh + bh)
= 2(2 × 7 + 2 × 10 + 7 × 10)
= 2(14 + 20 + 70)
= 2(104)
A = 208 m2
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,
- l = 9 m
- b = 6 m
- h = 7 m
SA = 2(lb + lh + bh)
= 2(9 × 6 + 7 × 9 + 6 × 7)
= 2(54 + 63 + 42)
= 2(159)
A = 318 m2
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,
- l = 21 cm
- b = 15 cm
- h = 18 cm
LSA = 2h (l+ b)
= 2 × 18 (21 +15)
= 36 × 36
LSA = 1,296 cm2
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,
- l = 7 m
- b = 6 m
- h = 5 m
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,
- l = 15 cm
- b = 10 cm
- h = 13 cm
LSA = 2h (l+ b)
= 2 × 13 (15 + 10)
= 26 × 25
LSA = 650 cm2
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,
- l = 8 m
- b = 5 m
- h = 9 m
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