# Rectangular Prism and its Solved Examples

3 min readHave you ever wondered about the shape of books, bricks, boards, mobiles, or laptops? These are real-life examples of a rectangular prism. You might question that these objects are examples of cuboids. So let me tell you that a rectangular prism is also a cuboid. A rectangular prism is a 3-dimensional geometrical figure which is solid in shape and has six rectangular faces such that the opposite pairs of the geometrical figure are congruent to each other. In this module, we will learn in detail about the volume of the rectangular prism and its surface area. We will also go through some examples of the volume of the rectangular prism and the surface area of the rectangular prism so that these concepts become very easy for you.

**What Do You Mean by the Volume of a Rectangular Prism?**

The amount of space which is contained within a rectangular prism is known as the volume of a rectangular prism. We know that the base area of the rectangular prism is a rectangle and the area of a rectangle is the product of its length and its breath. This area when multiplied by the height of the rectangular prism gives us the volume of the rectangular prism. Thus, the volume of a rectangular prism = Length * Breadth * Height.

If we notice carefully, the formula of the volume of a rectangular prism resembles the formula of the volume of a cuboid.

**What Do You Mean by the Surface Area of Rectangular Prism?**

The total area occupied by the rectangular prism is known as the surface area of the rectangular prism. There are numerous practical life uses of the calculation of the surface area of rectangular prism. In rectangular prisms, we have two types of surface area, namely, the lateral surface area and the total surface area.

Lateral Surface Area: It is the sum of the surface area of all the sides of the rectangular prism except the bases. The formula of the lateral surface area of the rectangular prism is given as follows:

(Breadth * Height) + (Breadth * Height) + (Height * Length) + (Height * Length) =

2 { (Breadth * Height) + (Height * Length) }

Total Surface Area: It is the sum of the surface area of the sides of the rectangular prism. The formula of the total surface area of the rectangular prism is given as follows:

(Length * Breadth) + (Length * Breadth) + (Breadth * Height) + (Breadth * Height) + (Height * Length) + (Height * Length) =

2 { (Length * Breadth) + (Breadth * Height) + (Height * Length) }

**Solved Sums for the Volume and the Surface Area of a Rectangular Prism**

- Find the volume of a matchbox which resembles the shape of a rectangular prism having length 5 cm, breadth 2 cm and height 2 cm respectively.

Solution: We know that the formula of the volume of a rectangular prism is given as: Length * Breadth * Height

Thus the volume of the matchbox = Length * Breadth * Height = 5 * 2 * 2 = 20 cubic cm.

- You have a red brick with yourself. This brick resembles the shape of a rectangular prism having length 5 cm, breadth 2 cm, and height 2 cm respectively. You are required to find the lateral surface area and the total surface area of the brick.

Solution: We know that the formula of the lateral surface area of rectangular prism = 2 (bh + hl) and the total surface area of rectangular prism = 2 (lb + bh + hl)

Thus lateral surface area of brick = 2 (2* 2 + 2* 5) = 2 (4 + 10) = 2* 14 = 28 square cm.

Total surface area of brick = 2 (2* 5 + 2* 2 + 2* 5) = 2 (10 + 4 + 10) = 2* 24 = 48 square cm.

The concepts of volume of a rectangular prism and the surface area of a rectangular prism can be a bit tricky at advanced levels. If you want to learn these concepts in detail and in an interesting and fun way, visit Cuemath and solve all your doubts.

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