Area of a Prism

A prism refers to any three dimensional solid figure comprising flat surfaces on one or more sides with two or more identical bases and the same cross-section throughout. A prism can have any number of sides as long as there are at least two identical bases. A prism includes a subset of numerous shapes like a cone, a cube, a triangle, a rectangle or even a cylinder. The key to detecting a prism is to look out for the identical bases and check if the figure has three dimensions. The identical bases of a prism are called parallelograms. From multistoried buildings to ice cones, from tents to tomatoes, there are plenty of examples of objects with the prismatic shape around us. 

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Types of Prisms

The unique feature of a prism is if it is cut from the middle or basically at the intersection. The cross-section of the object will be parallel to the base. This means that the cross-section of the prism will be uniform throughout. Given that most prisms are polygonal, depending on the shape of the cross-section, there are mainly two types of prisms, regular and irregular prisms. 

A regular prism may be defined as a prism whose base corresponds to a regular polygonal shape, for example, a square, a circle, a triangle, etc. Let’s take the example of a rod. Cylindrical in shape, if this rod is cut in the middle, we will obtain a perfect circle which will be identical to its circular base. Similarly, if you were to cut out a plateau in the middle, you’d get a quadrilateral which would be parallel to its base. 

On the contrary, an irregular prism has every other property of a prism but it doesn’t resemble a regular polygon. This is to say that it does not have a rectangle or a triangle or any other regular polygonal shape as its base. Remember those fascinating kaleidoscopes that we all loved to buy from the fairs? Many of them had interesting shapes like hearts, stars, bubbles, etc. Now, these are not regular polygons so prisms with irregular shapes base are called irregular prisms. 

Now that we know the definition of a prism, let us move to find out the surface area of the prism. 

Area of Prism

As a three dimensional figure, the area of a prism is calculated in terms of the surface area of the prism, which is basically the sum of the area of all its faces. We know in the case of a two-dimensional figure, we find out the area by multiplying the sides of the figure. In case of a three-dimensional figure like a prism, we calculate the area of the prism by including the height of the object as well. 

We know that the defining feature of a prism is that it has two identical bases, irrespective of the kind of prism. Now, if the area of prism definition reflects, the sum of the surface area of all its faces, then we can simply double up the area of the bases and add the product of the rest of the dimensions. Let us illustrate this better with the area of the prism formula. 

The surface area of prism formula may be defined as 2 x area of base + (perimeter of base x height)

Area of Prism Example

If we take the example of a rectangular prism, then the area of prism formula would read like:

2 x Length x Breadth + 2( Length + Breadth) x Height

Let us now understand the area of prism formula in this case with the figure :

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Area of the base is length x breadth, so we simply need to double it up for the top and the bottom surfaces. 

Then we sum up the perimeter of the base by adding the length and the breadth and again double it up for the parallel sides. Finally, we multiply this with the height to account for the third dimension and voila! We have our surface area of prism for a rectangular prism. 

Area of Prism Solved Example

How can we calculate the surface area of a prism for a triangular prism?

The area of prism formula is 2 x Length x Breadth + 2( Length + Breadth) x Height

On a similar count, we can combine the area of the prism formula to a triangular in order to find the surface area of prism in this case. 

The formula to be used here would be Area of the triangular base + 2( perimeter of the sides) x height

Hence, the area of the base can be evaluated as : H x B + 2(S1+S2+S3) x H

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FAQ (Frequently Asked Questions)

1. What is Meant by the Area of Prism?

Do not let the complicated surface area of the prism formula confuse you, the area of prism is simply the count of total space that is enclosed by a three dimensional object which has a prismatic shape. We can deduce the surface area of prism by using a simple area of prism formula which is: 

The area of prism formula may be defined as : 2 x area of base + (perimeter of base x height)

The reason why we use the height of the prism as well is because it is a 3-dimensional object and hence, it has three measurements. This is different from 2-dimensional figures which have only two measurements.

2. What are the Different Categories of Prisms, Besides the Regular and Irregular Prisms?

Depending on the shapes of their bases, prisms are primarily divided into regular and irregular prisms. However, prisms are further divided into two categories based on how the bases and the edges are joined together. 

Right Prism refers to those prisms whose surfaces and the joining edges are at right angles or are perpendicular to each other. A rectangular tissue box is a good example for such prisms. 

Oblique Prisms are those whose faces and joining edges are not entirely perpendicular to each other. A cylinder is an example of an oblique prism. 

Further, prisms can also be categorised as triangular prism, rectangular prism, hexagonal prism, pentagonal prism and others depending on the shape of their bases.