Table of Contents

Last modified on August 3rd, 2023

A rectangular prism is a three-dimensional solid bounded by 6 rectangular faces, where the 2 faces are the bases (top face and bottom face), which are congruent, and the rest 4 are lateral faces. It also has 8 vertices and 12 edges.

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.

**Right Rectangular Prism**– It has all the faces perpendicular. Thus every face is rectangular. A**cuboid**is a right rectangular prism as all its angles are right angles. Thus, a cuboid also holds all the above features except the oblique rectangular prism. The faces of a right rectangular prism are rectangles.**Oblique Rectangular Prism**– Its lateral faces are not perpendicular to its bases. So, every lateral face is parallelogram-shaped. The faces of an oblique rectangular prism are parallelograms.

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 m^{2}, cm^{2}, mm^{2}, and in^{2}. 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 total and lateral surface area of a rectangular prism is given below:

**Lateral Surface Area ( LSA) = 2(wh + hl), **here,

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

Let us solve an example to understand the concept better.

**Find the lateral**

Solution:

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 cm^{2}

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 cm^{2}

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.**

Solution:

As we know,

Volume (*V*) = *l* × *w* × *h*, here *l* = 9 cm, *w* = 6 cm, *h* = 15 cm

∴ *V* = 9 × 6 × 15

= 810 cm^{2}

Finding the diagonal of a rectangular prism when **ALL 3** **DIMENSIONS** are known

**Find the diagonal of a rectangular prism with dimensions of 6 cm, 5 cm, and 4 cm.**

Solution:

As we know,

The equation of body diagonal of a rectangular prism is 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

**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