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# Rectangular Prism

Geometry is the study of shapes and configuration of objects. It is one of those important branches of mathematics that have practical and real life usage.

Rectangular prisms is a three dimensional solid shape. It is a polyhedron with two congruent and parallel bases. This type of prism has six faces and all the faces of the prism are rectangles in shape.Rectangular prism is just like a cuboid.

The geometrical shapes are broadly classified on the basis of thier number of dimensions.

1) zero-dimensional Shape- Point.

2)
One-dimensional Shape - Line and line segment.

3)
Two-dimensional Shapes - Square, rectangle, triangle, circle, rhombus, parallelogram, trapezium, ellipse, parabola etc.

4)
Three-dimensional Shapes - Cube, cuboid, sphere, cone, pyramid, cylinder, hemisphere, ellipsoid etc

 Related Calculators Calculate Volume of Rectangular Prism Rectangular Prism Calculator Calculate Surface Area of a Rectangular Prism Convert Polar to Rectangular Calculator

## What is a Rectangular Prism?

Rectangular prisms is a three dimensional solid shape. This type of prism has six faces and all the faces of the prism are rectangles in shape. Basically in rectangular prism, both bases must be rectangle. Eventually, other lateral faces will also be rectangles. A rectangular prism is also known as a cuboid. In this section, we will discuss about rectangular prism and the formulas used to find the volume and surface area of a rectangular prism.

Lets discuss about prisms. The prisms are very commonly used in mathematics. A prism is a solid shape that has two flat congruent bases. It has lateral surfaces that join two bases together. Also, the cross sections of prism parallel to the base at each point are congruent. Two prisms are demonstrated in the image attached below :

## Formula for Rectangular Prism

Below are some formulas for rectangular prism:

Let 'l', 'w' and 'h' be the length, width and height of the rectangular prism.
• Lateral surface area of rectangular prism = Ph = 2(l + w)h
• Area of a Rectangular Prism = 2(lh + wh + lw)
• Volume of rectangular prism = lwh
• Diagonal of a rectangular prism = $\sqrt{l^2 + w^2 + h^2}$

## Volume of Rectangular Prism

Volume of a Rectangular Prism is a measurement of the occupied units of a Rectangular Prism. The volume of a Rectangular Prism is represented by cubic units. It is also defined as the number of units used to fill a Rectangular Prism.

### Volume of a Rectangular Prism Formula:

The volume of the rectangular prism is equal to the area of the base times its height.

Volume of rectangular prism = Length $\times$ Width $\times$ Height

### Finding Volume of a Rectangular Prism:

Let us find the volume of the rectangular prism, by using the given figure.

Given:

Length of the rectangular prism = 12 cm

Height of the rectangular prism = 5 cm

Width of the rectangular prism = 6 cm

Volume formula for rectangular prism = Height x Width x Length

= 5 $\times$ 6 $\times$ 12

= 360

$\therefore$ The volume of the rectangular prism is 360 cm3.

## Lateral Area of a Rectangular Prism

The lateral surface area of solid is the sum of the surface area of all its faces without the base of the solid. The lateral surface area of any right rectangular prism is equal to the perimeter of the base times the height of the prism.

$\Rightarrow$ Lateral surface = PH
Where, P is the perimeter of a base and H be the height of the prism.

Perimeter of the rectangular prism is,

P = 2(L + W)

Where, 'L' and 'W' be the length and width of the prism.
Lateral surface area of rectangular prism = PH = 2(L + W)H

Where, 'L', 'W' and 'H' be the length, width and height of the prism.

## Surface Area of a Rectangular Prism

Surface Area of a Rectangular Prism is the measure of how much exposed area a prism has. Surface Area is expressed in square units. Surface area of rectangular prism is the sum of the lateral surface area and twice the base area of the rectangular prism.

Surface Area, SA = Lateral surface area + Twice the base area

SA = 2(l + w)h + 2lw

= 2lh + 2wh + 2lw

= 2(lh + wh + lw)

### Surface Area of Rectangular Prism Formula:

Area of a Rectangular Prism = 2(lh + wh + lw)

where, l - Length of Prism
w - Width of Prism
h - Height pf Prism

## Right Rectangular Prism

### A prism with rectangular bases is a rectangular prism. A right rectangular prism is a prism which has six faces that are rectangles and all angles are right angles.

Rectangular prism vertices = 8

Rectangular prism edges = 12

Rectangular prism faces = 6 (including bases)

## Oblique Rectangular Prism

A prism in which the bases are not perpendicular to each other is called an oblique prism. A rectangular prism with bases that are not aligned one directly above the other is oblique rectangular prism.

## Rectangular Prism Examples

Given below are some of the examples on Rectangular Prism.

### Solved Examples

Question 1: Find the lateral surface area of a rectangular box in the shape of prism whose dimensions are 12 cm $\times$ 14 cm $\times$ 10 cm.
Solution:
Given: Dimensions of rectangular prism are,
Length (L) = 12 cm
Width (W) = 14 cm
Height (H) = 10 cm

Step 1: Perimeter of a rectangular prism (P) = 2(L + W)

=> P = 2(12 + 14)

= 52

=> P = 52 cm

Step 2: Lateral surface area of rectangular prism (LSA) = PH

=> LSA = 52 $\times$ 10

= 520

Hence, the lateral surface area of the rectangular box is 520 cm2

Question 2:

Find the surface of the rectangular prism, by using the given figure.

Solution:

Given:

Length of the rectangular prism = 8

Height of the rectangular prism = 4

Width of the rectangular prism = 6

Surface area = 2wl + 2lh + 2hw

= 2 $\times$ 6 $\times$ 8 + 2 $\times$ 8 $\times$ 4 + 2 $\times$ 4 $\times$ 6

= 96 + 64 + 48

= 208

Therefore, the surface area of a rectangular prism is 208 square units.

 More topics in Rectangular Prism Volume of a Rectangular Prism Surface Area of a Rectangular Prism
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