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 2 opposite side deals with are identical. Favor all three-dimensional shapes, a rectangular prism additionally has volume and also surface area. A rectangle-shaped prism is likewise known together a cuboid. Let us learn more about a rectangle-shaped prism in addition to the formulas to uncover 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 rectangle-shaped prism is a prism who bases (both its top face and bottom face)are rectangles.It has 6 encounters in complete out ofwhich there room 3 bag of similar opposite faces. I.e., every two opposite encounters are similar in a rectangle-shaped prism. It has three dimensions, length, width, and also height. Some examples of a rectangle-shaped prism in genuine life are rectangular tissue boxes, school notebooks, laptops, fish tanks, large structures such as cargo containers, rooms,storage sheds, etc. In the number below, you have the right to see exactly how a rectangle-shaped prism looks like and how its net (the shape created by it when its faces are opened) look at like.

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Types ofRectangular Prisms


There are two varieties of rectangular prisms that room classified depending on the shape of the side faces (or) the edge made through the side deals with with the base.

Right rectangular prismOblique rectangular prism

A right rectangle-shaped prism has actually its side faces perpendicular to each of that is bases. In this,all side deals with are rectangles. One oblique rectangle-shaped prism is a prism that is not a right rectangular prism and its side encounters are parallelograms. In general, a rectangular prism without any type of specifications is a right rectangle-shaped prism.

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Properties ofRectangular Prism


Here are the properties of a rectangular prism that follow that is definition.

A rectangle-shaped prism has actually 6 faces, 8 vertices, and also 12 edges.Its base and top are always rectangles.The side deals with are rectangles for a right rectangular prism whereas the side faces of one oblique rectangle-shaped prism room parallelograms.It has actually 3 dimensions, length, width, and height.

Formulas ofRectangular Prism


In this section, we will find out the formulas of the volume and surface area that a rectangular prism. Because that both that these, allow us take into consideration a rectangle-shaped prism of length 'l', width 'w', and also height 'h'. Follow me these dimensions, let united state assume that 'l' and also 'w' room the size of the base. Below are the formulas because that the volume and also surface area of a rectangle-shaped prism.

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Let united state see just how to derive these formulas.

Volume of rectangular Prism

The volume that a rectangular prism is the an are that is inside it. We understand that the volume of any prism is acquired by multiply its basic area through its height. Here,

The elevation of the rectangle-shaped prism = h

Thus, the volume of the rectangle-shaped prism, V = lw× h = lwh.

Surface Area ofRectangular Prism

There space two types of surface ar area the a rectangular prism, one is the total surface area (TSA) and also the other is the lateral surface ar area (LSA).

TSA that a rectangle-shaped prism is the sum of the locations of all of its faces.LSA the a rectangular prism is the amount of the areas of all its side deals with (no bases).

We deserve to calculate the locations of the side encounters of a rectangular prism using its net as shown below.

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Using the above figure,

The complete surface area (TSA) that a rectangle-shaped prism

= The sum of locations of every faces

= lw + lw +wh + wh + hl + hl

= 2 (lw + wh + hl)

The lateral surface area (LSA) the a rectangular prism

= The amount of areas of side faces

= wh + wh + hl + hl

= 2 (wh + hl)

We will check out the applications of these volume and surface area recipe of a rectangle-shaped prism in the ar below.

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Example 2:A gift is packed in a rectangle-shaped box (rectangular prism)of size 15 in, 10 in, and also 8 in and also it demands to be wrapped through gift paper. Just how much gift document is forced to pave the gift box?

Solution:

The size of the offered gift box are,

length, together = 15in

width, w = 10in

height, h = 8in

To find the lot of gift document required, we need to find the full surface area that the box.