Table of Contents
Last modified on August 26th, 2024
A rectangular prism is a three-dimensional solid bounded by faces, edges, and vertices.
Due to its shape, a rectangular prism is also called a cuboid. Some real-life examples of rectangular prisms are a shoe box, an ice cream bar, or a matchbox.
A rectangular prism is of 2 types based on the angle formed by the lateral faces at the bases. They are right and oblique rectangular prisms.
The surface area of a rectangular prism is the entire space occupied by its outermost layer (or faces). It is expressed in square units such as m2, cm2, mm2, and in2. We can calculate 2 types of surface areas in a rectangular prism.
The lateral surface area (LSA) of a rectangular prism is only the sum of the surface area of all its faces except the bases. The formula to calculate the lateral surface area of a rectangular prism is given below:
Lateral Surface Area (LSA) = 2(wh + hl), here, l = length, w = width, h = height
The total surface area (TSA) of a rectangular prism is the sum of the lateral surface area and twice the base area. The formula to calculate the TSA of a rectangular prism is given below:
Total Surface Area (TSA) = 2(lw + wh + hl), here l = length, w = width, h = height
Let us solve an example to understand the concept better.
Find the lateral and total surface area of a rectangular prism with length 16 cm, width 12.5 cm, and height 10 cm.
As we know,
Lateral Surface Area (LSA) = 2(wh + hl), here l = 16 cm, w = 12.5 cm, h = 10 cm
∴ LSA = 2(12.5 × 10 + 10 × 16)
= 570 cm2
Total Surface Area (TSA) = 2(lw + wh + hl), here l = 16 cm, w = 12.5 cm, h = 10 cm
∴ TSA = 2(16 × 12.5 + 12.5 × 10 + 10 × 16)
= 970 cm2
The volume of a rectangular prism is its space in the three-dimensional plane. The formula to calculate the volume of a rectangular prism is given below:
Volume (V) = l × w × h, here l = length, w = width, h = height
Find the volume of a right rectangular prism. Dimensions of a rectangular prism are 9 cm long, 6 cm wide, and 15 cm high.
As we know,
Volume (V) = l × w × h, here l = 9 cm, w = 6 cm, h = 15 cm
∴ V = 9 × 6 × 15
= 810 cm2
There are two types of diagonals found in a rectangular prism:
Face Diagonals
A face diagonal is a line segment that connects two opposite corners (or vertices) on any face of a rectangular prism.
Each face of a rectangular prism has 2 diagonals. Since the prism has 6 faces, the total number of face diagonals is 6 × 2 = 12.
Space Diagonals
A space diagonal is a line segment that connects two opposite corners (or vertices) of a rectangular prism, passing through its interior. Therefore, each rectangular prism has 4 space diagonals.
Thus, each rectangular prism has 4 space diagonals.
The formulas to calculate the length of face diagonals and space diagonals of a rectangular prism are given below:
Find the diagonal of a rectangular prism with dimensions of 6 cm, 5 cm, and 4 cm.
As we know,
The equation of the space diagonal of a rectangular prism is the same as that of a cuboid.
∴ Diagonal (D) = ${\sqrt{l^{2}+w^{2}+h^{2}}}$, here l = 6 cm, w = 4 cm, h = 5 cm
${\therefore D=\sqrt{6^{2}+4^{2}+5^{2}}}$
= 77 cm
The perimeter of a rectangular prism is the sum of the lengths of all the edges. The formula to calculate the perimeter of a rectangular prism is:
Perimeter of a rectangular prism = 4(l + w + h) units, here l = length, w = width, h = height
Calculate the perimeter of a rectangular prism with the dimensions 11 cm × 5 cm × 4 cm.
As we know,
The perimeter of a rectangular prism = 4(l + w + h) units, here l = 11 cm, w = 5 cm, h = 4 cm
∴ P = 4(11 + 5 + 4)
= 80 cm
The net of a rectangular prism is the 2D shape we get when the 3D-shaped rectangular prism is unfolded. This view helps us to identify the sides of the rectangular prism.
A rectangular prism with three different lengths has 54 distinct nets. Here, a few different nets of a rectangular prism are shown.
Last modified on August 26th, 2024