A rectangular prism is a three-dimensional shape, having six faces, where all the faces (top, bottom, and lateral faces) of the prism are rectangles such that every two opposite side faces are identical. Like all three-dimensional shapes, a rectangular prism also has volume and surface area. A rectangular prism is also known as a cuboid. Let us learn more about a rectangular prism along with the formulas to find its volume and surface area.
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|1.||What IsRectangular Prism?|
|2.||Types ofRectangular Prisms|
|3.||Properties ofRectangular Prism|
|4.||Formulas ofRectangular Prism|
|5.||FAQs on Rectangular Prism|
What IsRectangular Prism?
A rectangular prism is a prism whose bases (both its top face and bottom face)are rectangles.It has 6 faces in total out ofwhich there are 3 pairs of identical opposite faces. i.e., every two opposite faces are identical in a rectangular prism. It has three dimensions, length, width, and height. Some examples of a rectangular prism in real life are rectangular tissue boxes, school notebooks, laptops, fish tanks, large structures such as cargo containers, rooms,storage sheds, etc. In the figure below, you can see how a rectangular prism looks like and how its net (the shape formed by it when its faces are opened) looks like.
Types ofRectangular Prisms
There are two types of rectangular prisms that are classified depending on the shape of the side faces (or) the angle made by the side faces with the base.Right rectangular prismOblique rectangular prism
A right rectangular prism has its side faces perpendicular to each of its bases. In this,all side faces are rectangles. An oblique rectangular prism is a prism that is NOT a right rectangular prism and its side faces are parallelograms. In general, a rectangular prism without any specifications is a right rectangular prism.
Properties ofRectangular Prism
Here are the properties of a rectangular prism that follow its definition.A rectangular prism has 6 faces, 8 vertices, and 12 edges.Its base and top are always rectangles.The side faces are rectangles for a right rectangular prism whereas the side faces of an oblique rectangular prism are parallelograms.It has 3 dimensions, length, width, and height.
Formulas ofRectangular Prism
In this section, we will learn the formulas of the volume and surface area of a rectangular prism. For both of these, let us consider a rectangular prism of length 'l', width 'w', and height 'h'. Along these dimensions, let us assume that 'l' and 'w' are the dimensions of the base. Here are the formulas for the volume and surface area of a rectangular prism.
Let us see how to derive these formulas.
Volume of Rectangular Prism
The volume of a rectangular prism is the space that is inside it. We know that the volume of any prism is obtained by multiplying its base area by its height. Here,The height of the rectangular prism = h
Thus, the volume of the rectangular prism, V = lw× h = lwh.
Surface Area ofRectangular Prism
There are two types of surface area of a rectangular prism, one is the total surface area (TSA) and the other is the lateral surface area (LSA).TSA of a rectangular prism is the sum of the areas of all of its faces.LSA of a rectangular prism is the sum of the areas of all its side faces (no bases).
We can calculate the areas of the side faces of a rectangular prism using its net as shown below.
Using the above figure,
The total surface area (TSA) of a rectangular prism
= The sum of areas of all faces
= lw + lw +wh + wh + hl + hl
= 2 (lw + wh + hl)
The lateral surface area (LSA) of a rectangular prism
= The sum of areas of side faces
= wh + wh + hl + hl
= 2 (wh + hl)
We will see the applications of these volume and surface area formulas of a rectangular prism in the section below.
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Example 2:A gift is packed in a rectangular box (rectangular prism)of dimensions 15 in, 10 in, and 8 in and it needs to be wrapped with gift paper. How much gift paper is required to wrap the gift box?
The dimensions of the given gift box are,
length, l = 15in
width, w = 10in
height, h = 8in
To find the amount of gift paper required, we need to find the total surface area of the box.