In geometry, we study about shapes and figures which are referred as geometrical shapes. The geometric information that remains after removing scale, location and orientation from a geometrical object, is known as a geometrical shape. Any closed figure is referred to as a shape like triangle, square, octagon, pentagon etc. That is, a geometric shape has to be a figure bounded from all directions. In other words, there must be at least three sides for a shape to be called a geometric shape. Also, no side has to have an open end. We are going to learn about irregular shapes and their properties with the help of example in this article.

## Definition of Irregular Shapes

These shapes are classified on many different bases of which one is length of sides. When the length of all sides of any shape is same, we call it a regular shape. When the sides of a shape are unequal, we call it an irregular shape.

This image shows a regular pentagon, a regular hexagon and a regular octagon. It is clear that all sides of given shapes are equal and also all interior angles hence will also be equal.

This image shows an irregular pentagon, an irregular hexagon and an irregular octagon. Clearly, the sides of the shapes are of unequal lengths.

## Perimeter of Irregular Shapes

Perimeter is the sum of the length of all sides of any closed shape. So, perimeter of any irregular shape can be easily calculated by simply adding the lengths of all sides of that shape. This proves that perimeter is irrespective of the type of shape given. The only difference is that we can multiply the length of one side of a regular shape with the number of sides it has to obtain its perimeter but we have to add up each side separately in case of irregular shapes to obtain the perimeter.

## Area of Irregular Shapes

To find the area of any irregular shape we should break it in regular shapes if possible and then find individual area of each break up. In the end we can add all the areas obtained to find the area of the require shape. This concept is used as the area of the shape is not affected by breaking it up into smaller pieces. This is the only possible method to find area of any irregular shape.

## Volume of Irregular Shapes

The only possible method to find volume of any irregular shape is to break it in regular shapes if possible and then find individual volumes of each break up part. Finally, in the end we can add all the volumes of the divided shapes so obtained to find the total volume of the given shape. This concept is applicable because of the fact that volume of any shape does not get affected by reshaping or transforming neglecting the minor error of loss of negligible matter in the process of transformation or breaking up.

## How to Draw Irregular Shapes

Drawing an irregular shape is never a problem as being irregular gives it an advantage of not being precise at all. So one can roughly draw an irregular shape easily may it be a two-dimensional shape or a three-dimensional shape. Drawing an irregular shape is not that tedious job but yes if there is a pattern followed to make one then it should be maintained in order to maintain the correct shape as required and given in the problem. In general, we can say that irregular shapes can be drawn easily at times.

## Irregular Shapes Examples

Let us look at some examples to understand the concepts better.
Example 1:

Find the area of the figure given below

Solution:

We know that area of a rectangle is the product of its two consecutive sides. There are two ways of solving the given problem.

First Way:

Complete the whole rectangle. Find the area of complete rectangle and the smaller rectangle. Subtract the two to get the actual area

Area of full rectangle = 6 $\times$ (4 + 3) = 6 $\times$ 7 = 42 sq cm

Area of small cut out rectangle = 2 $\times$ 3 = 6 sq cm.

Required area = 42 – 6 = 36 sq cm.

Second Way:

The second method is to break the rectangle in two rectangles from the line of disconnection and then find the individual areas of the two rectangles. Finally add them to obtain the required area.

Area of bigger rectangle = (6 – 2) $\times$ (4 + 3) = 4 $\times$ 7 = 28 sq cm

Area of smaller rectangle = 2 $\times$ 4 = 8 sq cm

Required area = 28 + 8 = 36 sq cm

It can be seen that in both the cases the answer is the same which implies that both the methods are correct.
Example 2:

Find the perimeter of the shape below

Solution:

Here two sides are missing. Let us first determine that.

x = 10 – 4 – 5 = 1 ft

y = 8 – 1 – 2 = 5 ft

We know that perimeter is sum of all sides of the shape.

Perimeter = 10 + 5 + 5 + 2 + 1 + 1 + 4 + 8 = 36 ft.

So, once the concepts are clear and we know the formulas for all basic regular or standard shapes then given any type of problem n irregular shapes, we can solve it accurately without any hesitation.