Area of Irregular Shapes

Measuring the area of irregular shapes feels tricky because unlike regular shapes there are no specific formulas to calculate the area of irregular shapes. But there are various methods to calculate the area of irregular shapes. In this article, we will cover these methods in detail along with examples to help you understand them better. Let’s start by understanding what irregular shapes are and why it is important to learn these methods.

Table of Contents

• What are Irregular Shapes?
• Methods to Determine Area of Irregular Shapes
• Examples on Finding Area of Irregular Shapes
• Applications of Estimating the Area of Irregular Shapes

What are Irregular Shapes?

Irregular shapes are figures that have no definite symmetry and cannot be categorised under any two dimensional or three dimensional shapes based on their characteristics and properties. Finding the area of regular shapes like cube, circle, rectangle, etc is easier. Whereas determining the area of irregular shapes requires understanding of some methods.

Methods to Determine Area of Irregular Shapes

Here are a few methods you can use to calculate area of irregular shapes easily:

Method 1: Counting Squares Method
1. Place the shape on the grid.
2. Count the number of squares occupied by the shape.
 
Method 2: Decomposition Method
1. Identify the shapes combined to form the irregular shape.
2. Apply the area formulas used for individual shape.
3. Combine the sum of all areas to get the final area of the irregular shape.


Method 3: Enclosing Method
1. Draw the smallest rectangle around the shape that encloses the shape.
2. Calculate the area of that rectangle.
3. Subtract the area left outside the shape from the area of the rectangle.

Examples on Finding Area of Irregular Shapes

Example 1: Find the area of an irregular shape that covers 19 squares on a grid.
Solution: The area of the irregular shape is the number of squares it occupies. 
Therefore the area of the shape = 19 sq units.

Example 2: Compute the area of an irregular shape using decomposition method.
Solution: The given shape is a combination of a square and a rectangle.
Therefore, Area of irregular shape = Area of square + Area of rectangle

Area of irregular shape = 4 x Side + Length x Breadth

Example 3: A t-shaped figure is formed using a vertical rectangle and a horizontal rectangle. The length and breadth of first rectangle is 5cm and 2cm whereas the second is 2cm and 6cm. Find its area.
Solution: The given figure is a combination of two rectangles.
Therefore, Area of irregular shape = Area of rectangle 1 + Area of rectangle 2
Area of rectangle 1 = L x B = 5 x 2 = 10cm2
Area of rectangle 2 = L x B = 2 x 6 = 12cm2
Combining both we get, Area of the t-shaped figure= 10 + 12 = 22cm2

Applications of Estimating the Area of Irregular Shapes

The methods for estimating the area of irregular shapes are applied in many fields in real-life. Here are a few examples of how we use these methods in our day to day life:

1. In geography, the area of an irregular piece of land is calculated using these methods.

2. In biology this concept is applied to find areas of many real-life objects like leaf, cell, etc.

3. In construction and architecture areas of many irregular spaces are calculated using these formulas.