Right Rectangular Prism

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Prisms are solid shapes with identical polygon ends and flat parallelogram sides.

Prisms are of different types named as triangular prisms, square prisms, rectangular prisms, pentagonal prisms, hexagonal prisms etc. A rectangular prism is of two types. They are the right rectangular prism and oblique rectangular prism. In this article, we will discuss rectangular prisms, their properties, formulas to calculate the area and volume of a prism.

Let us learn more about rectangular prism, right rectangular prism, cuboids, and cubes with the help of Rectangular Prism.


Definition of Right Rectangular Prism

A prism having a  rectangular base is called a rectangular prism. A right rectangular prism is a prism that has six faces and all the faces are rectangles. All angles formed are right angles.

Rectangular prism shape consists of the following properties:

Vertices of a rectangular prism = 8

Edges of a rectangular prism = 12

Faces of a rectangular prism= 6 (including bases)

The below diagram represents a right rectangular prisms

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Rectangular Prism Examples

Examples of rectangular prism shaped objects are Rectangular tissue box, school notebooks, binders, laptops, doors, containers, cabinets, mobiles, cereal boxes, fish tanks etc.

Large structures such as cargo containers, buildings, storage sheds, and skyscrapers are also an example of a rectangular prism.


Attributes of a Rectangular Prism

  • A rectangular prism has 6 faces(each of the faces is rectangular).

  • It has 12 sides and 8 vertices.

  • The pairs of opposite faces of a rectangular prism are equal.

  • There are two types of rectangular prisms named a right rectangular prism and non-right rectangular prisms ( also known as an oblique rectangular prism).

Right Rectangular Prism Formula

Lateral Surface Area of a Rectangular Prism

The lateral surface area of a rectangular prism is the sum of the surface area of all its faces excluding the base of the rectangular prism. The lateral surface area of any right rectangular prism is calculated using the perimeter of the base times the height of the prism.

Therefore, the lateral surface =P.h square units 

Where P  is the perimeter of a base

h be the height of the prism

Therefore, the lateral surface area of a rectangular prism =2(l+w)h square units


Rectangular Prism Surface Area

The surface area of a rectangular prism is the measure of how much exposed area a prism covers. It is expressed in square units. The surface area of a rectangular prism is the sum of the lateral surface area along with twice the base area of the rectangular prism.

Surface area of a rectangular prism = sum of surface area of six faces =lw+lw+wh+wh+lh+lh=2(lw+wh+lh) square units 

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Rectangular Prism Volume

The volume of a rectangular prism is a measurement of how much volume is occupied by a rectangular prism. The volume of a rectangular prism is denoted by cubic units. It can also be defined as the number of units used to fill a rectangular prism.

The volume of the rectangular prism is calculated by using the area of the base times its height.

Hence, the volume of a rectangular prism formula is given by the formula

The volume of a Rectangular Prism (V)= lwh cubic units 

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How Does a Rectangular Prism Look Like?

Right Rectangular Prism

In a right rectangular prism:

  • The angles between the base and the sides are right angles.

  • All rectangular prism faces are rectangles.

  • Each corner of the prism is represented by a right angle.

  • All the base and top of the prism are congruent.

Right Prisms

A right prism is in the shape of a geometric solid that has a polygon as its base and vertical sides perpendicular to the base. The base and top surface are of the same shape and size. It is called a “right” prism because the angles between the base and sides are right angles. Examples of right prisms are a rectangular prism, a cube, a triangular prism and a cylinder.


Net of a Right Rectangular Prism:

The net of a 3D object is used to show the faces of that object when it is opened flat. We can form a right rectangular prism using its net as shown in the below diagram. Each face of the net is a rectangle that contains the right angles.

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Solved Examples:

1.Find the volume of a rectangular prism whose length, width, and height are 7cm, 6cm, and 4cm, respectively.

Sol: Given Length, l = 7 cm

Width, w = 6 cm

Height, h = 4 cm

The volume of a rectangular prism is, given by l.w.h

V = l x w x h cubic units

Put the value of l,w and h in the formula

V = 7 x 6 x 4 cm³

V = 168 cm³

Therefore, the volume of a rectangular prism is 168 cm³


2.Find the area of a rectangular prism whose length, width, and height are 7cm, 6cm, and 4cm, respectively.

Sol:Given:

Length, l = 7 cm

Width, w = 6 cm

Height, h = 4 cm

The formula to find the area of a rectangular prism is, 2(lh+wh+lw)

Put the value of l,w and h in the given formula

A=2(lh+wh+lw)

A=2(7x4+6x4+7x6)

A=2(28+24+42)

A=2(94)

A=188 sq.cm


3. Tim wanted to add soil to his gardening bed which resembles the shape of a rectangular prism and has the following dimensions:length = 8 ft, width = 4 ft, and height = 1 ft. Calculate the maximum amount of planting soil that can be used to fill the gardening bed?

Sol: Tim's gardening bed resembles that of a rectangular prism having the following dimensions:

Length, l = 8 ft

Width, w = 4 ft

Height, h = 1 ft

The maximum amount of planting soil that can be used to fill the gardening bed = Volume of the bed = l x w x h

After putting the value of l,w and h, 8 x 4 x 1 = 32 cubic feet.

Therefore 32 cubic feet of soil can be used.


Conclusion:

A right rectangular prism has six faces- the base, the top, and the four sides.

The base and top of the rectangular prism always have the same area, similar is the case for its pairs of opposite sides. A rectangular prism consists of 12 edges, 6 faces and 8 vertices.

Formula to Calculate Volume and Surface area is given as:

The volume of Rectangular Prism: V=lwh cubic units

Surface Area of Rectangular Prism: S =2(lw+lh+wh) square units.

FAQ (Frequently Asked Questions)

1. What is the Difference Between a Right Rectangular Prism and a Rectangular Prism?

Ans: A rectangular prism has a rectangular cross-section. It may not stand vertical if we make it stand on the cross-sectional base. A right rectangular prism has 6 faces, all the faces are in rectangular shape. The angles formed between the base and sides are right angles.

2. What are the Characteristics of a Rectangular Prism?

Ans: A rectangular prism has 8 vertices, 12 sides and 6 rectangular faces. All the pairs of opposite faces of a rectangular prism are equal. A rectangular prism has a rectangular cross-section.

3. How Many Bases are in a Rectangular Prism?

Ans: A rectangular prism consists of two rectangular bases.