Rectangular Prism

What is a Rectangular Prism?

A rectangular prism can be defined as a polyhedron with two congruent and parallel bases. It is also known as a cuboid. 


This geometric structure has six faces, all in the shape of a rectangle and a total of twelve edges. Due to its cross-section along the length, it is known to be a prism. Just like a triangle, square and pentagonal prism, rectangular prisms also have its surface area. The surface area of the prism is equal to the area of its net.


Nets of Rectangular Prisms: 

The surface area of an object is said to be equal to the number of square units needed to cover all of the surfaces of that object. The net of any geometrical is obtained when it is unfolded along its edges and its faces are laid out in a pattern in two dimensions.  Let's try and pull this rectangular prism apart to see what surfaces we need to cover! Once, you pull the surfaces completely apart you will see that Nets of rectangular prisms are made up of rectangular and square shapes.


Using a Net for Computing the Surface Area of a Rectangular Prism

Finding the areas of all of the rectangles and squares of the net of a rectangular prism and then adding these values of areas results in the surface area of the rectangular prism. 


Let’s take an example, consider the length of one side of the cube as 4 units. In this case, the surface area of one of its faces comes out to be 4 × 4 = 16 square units. With the help of the net, it can be seen that there are 6 faces in total. So. The total surface area, in this case, comes out to be 6 × 16 = 96 square units. 


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What is the Surface Area of a Rectangular Prism?

The surface area of a rectangular prism is equal to the total area of all six faces. If we have a cube, finding the area of one face allows you to find the total surface area of the geometric figure accuracy which will be six times the area of one face.


Surface Area of a Rectangular Prism Formula

For finding the surface area of rectangular prisms, the operation of both addition and multiplication takes place. For finding surface area we must know the width, length, and height of the rectangular prism and then apply the following formula: 

A = 2(width × length) + 2(length × height) + 2(height × width)

Abbreviations for width is w; for length is l, and for height is h. 

Now let’s recast the formula for a better understanding:

A = 2wl + 2lh + 2hw


Let’s take an example: You have been asked to gift wrap a box for a friend of yours. The gift box has 100 books of science jokes. Can you find the total number of books that can be accommodated in the box and the minimum amount of wrapping paper that would be needed? Do you know how many books are in the box? 


The dimensions of the box are: 

  • Width -- 30 cm

  • Length -- 15 cm

  • Height -- 20 cm

We will begin by using the surface area formula to estimate the minimum wrapping paper that will be needed. 


The next step is to build an equation for the surface area of the gift box which is in the shape of a rectangular prism: 


A = 2(width × length) + 2(length × height) + 2(height × width)


Abbreviations for width is w; for length is l; and for height is h. 

Now let’s recast the formula for a better understanding:

A = 2wl + 2lh + 2hw

.

The next step is to build an equation for the surface area of the gift box which is in the shape of a rectangular prism:

There A = 2 (wl + lh + hw)

A = 2 (30 ⋅ 15 + 15 ⋅ 20 + 20 ⋅ 30) 

A = 2 (450 + 300 + 600)

A = 2 (1,350)

A = 2,700 cm2

Therefore, the minimum gift wrap required is 0.27 m2 


Volume of a Rectangular Prism

Volume is the measure of 3-dimensional space an object takes up or occupies. Volume is measured in cubic units.


For example, the rectangular prism below has a volume of 18 cubic units because it is made up of 18unit cubes.

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For finding the volume of a rectangular prism, we need to first perform multiplication operation of the length of the rectangular prism to its width and then its height. 


Volume of rectangular prism= Length x width x height


Let’s take up an example here: The dimensions of a rectangular prism are given below, find the volume of the rectangular prism. 

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Volume= Length x Width x Height

Volume=3 x 2 x 3

Volume= 18 units


Rectangular prisms can be of two types, namely right rectangular prisms and non-right rectangular prisms.


What is Right Rectangular Prism?

A right rectangular prism is said to be a three-dimensional geometric figure which has=6 faces,12 edges, and 8 vertices. 

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The right rectangular prism can also be called a cuboid wherein each corner of the prism is at the right angle to each other. Each of the bases and the top show congruency, that is they are in the same shape and size.


Real - Life Examples of a Right Rectangular Prism:

Right rectangular prisms or cuboids can be easily seen all around us only if we have the eyes to look for them. Some of the examples of rectangular prisms are books, boxes, buildings, bricks, boards, doors, containers, cabinets, mobiles, and laptops.

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Parts of a Rectangular Prism

A rectangular prism has:

  • Bases

  • Lateral faces

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FAQ (Frequently Asked Questions)

1) What are the Properties of a Rectangular Prism?

Properties of a Rectangular Prism:

The properties of prisms are similar for every kind of prism with each one defined by the shape that makes up the base of the prism. Any polygon can be the base of a prism.


A rectangular prism consists of 8 vertices, 12 sides, and 6 rectangular faces. All the opposite faces of a rectangular prism are equivalent. A rectangular prism depicts a rectangular cross-section.


In a right rectangular prism, the following things can be observed:

  • There is an angle of 90 degrees between the base and the sides. 

  • All the 6 faces of the right rectangular prism are perfect rectangles in shape.

2) Is a Cube a Rectangular Prism?

Cuboid has a square cross-sectional area and a length perhaps different from the side of the cross-section.  It has 8 vertices, 12 sides, 6 faces.


It is like a cube, but one dimension is different from the other two.  All the angles are 90 degrees at the vertices or edges.  Cuboid stands vertically if you make it stand on the cross-section. A rectangular prism has a rectangular cross-section.  If you make it stand on the cross-sectional base,  it may not stand vertical.   It can be oblique or oblong. That is it may tilt to one side.  So all the vertical faces remain parallel and tilt in one direction at an angle.