Area of irregular shapes
To understand the concept of the area of irregular shapes, let us first see what is an irregular shape. A regular shape has equal sides and angles whereas an irregular shape is of any size and length. We may find regular shapes such as all the regular polygons around us. Square, regular pentagon, regular hexagon, etc are a few regular shapes to name a few. An irregular shape can be of any size and length. There are a lot of examples of irregular shapes around us. Any shape formed by the combination of polygons is an irregular shape.
Now that we have got an insight into irregular shapes, let's dig in more with examples to understand irregular shapes, and let's use that to find the area of irregular shapes.
1.  What Are Irregular Shapes? 
2.  Dividing Irregular Shapes Into Regular Shapes 
3.  How Do We Find Formula for Area of Irregular Shapes? 
What Are Irregular Shapes?
Irregular shapes are basically formed by a group of polygons and thus have a varying number of sides each of varying lengths. An irregular shape can therefore be decomposed into multiple regular shapes. From our everyday life, there can be different examples of irregular shapes:
 Observe the staircases of any building. The surface area of the staircase is an irregular shape composed of polygons like rectangles and squares.
 A playground in school with a running track is an irregular shape and is also a combination of regular shapes.
 Leaf plucked of a plant is an irregular shape that can be divided into many regular shapes.
Dividing Irregular Shapes Into Regular Shapes
Let's now see how can we decompose an irregular shape into regular shapes to find the area of irregular shapes. Here are a few irregular shapes to list a few:
 The regular polygons A, B, C, D, E, F, and G form the irregular shape in the figure given below:
 The regular polygons P, Q, R, S, T, and U come together to form an irregular shape. This is shown in the figure given below:
 An irregular shape is divided into small squares of the unit square area. A figure depicting this is given below:
How Do We Find Formula for Area of Irregular Shapes?
Method 1: To find the area of irregular shapes, we can divide the irregular shape into regular polygons and then find the area of each individual polygon.
Therefore, the area of the given irregular shape = Area of all the regular polygons that the irregular shape is divided into.
⇒ Area of the given irregular shape = area of A + area of B + area of C + area of D + area of E + area of F + area of G
Method 2: In some cases, the irregular shape is divided into small squares of the unit square area. The total number of unit squares falling within the shape determines the total area. Count the square as “1” if the shaded region covers more than half while calculating the area for a more accurate estimate. So in this case we get an approximate area of irregular shape. We can use this method for shapes with curves apart from perfect circles or semicircles and irregular quadrilaterals.
Therefore, the area of the given irregular shape = Sum of all the unit squares falling under the irregular shape.
Solved Examples

Example 1:
Find the area of the given irregular shape.
Solution:
To find the area of the irregular shape, we will add up the area of the shapes that come together to form this irregular shape:
Let's find the area of each shape first.
 Area of rectangle 'P' = Length × Breadth = 6 × 8 = 48 square units
 Area of semicircle 'Q' = πr^{2}/2 = 3.14 × 5^{2}/2 (taking π = 3.14 and using the fact that the diameter of the semicircle would be 10)
⇒ Area of semicircle 'Q' = 3.14 × 5^{2}/2 = 39.25 square units  Area of the triangle 'R' = 1/2 × Base × Height
⇒ Area of the triangle 'R' = 1/2 × 8 × 6 = 24 square units  Area of rectangle 'S' = Length × Breadth = 6 × 8 = 48 square units
Now let's find the area of the irregular shape using the area of the regular shapes:
Area of the given irregular shape = Area of the rectangle 'P' + Area of the semicircle 'Q' + Area of the triangle 'R' + Area of the rectangle 'S'.
⇒ Area of the given irregular shape = 48 + 39.25 + 24 + 48 = 159.25 square units.
Therefore, the area of the given irregular shape is 159.25 square units.

Example 2:
Find the area of the given shape.
Solution:
The given shape is divided into three rectangles, A, B, and C. Therefore, the area of the given shape is given as:
Area = Area of rectangle A + Area of rectangle B + Area of rectangle C
⇒ Area = 2 × 10 + 3 × 2 + 5 × 2
⇒ Area = 20 + 6 + 10 = 36 units^{2}.
FAQs on Area of Irregular Shapes
What Is an Irregular Shape?
Irregular shapes are basically formed by a group of polygons and thus have a varying number of sides each of varying lengths.
How Is an Irregular Shape Different From a Regular Shape?
A regular shape has equal sides and angles whereas an irregular shape is of any size and length.
What Types of Shapes Make an Irregular Shape?
Since an irregular shape is of any length and can have any number of sides, therefore, it is made up of a combination of a few regular polygons.
What Is the Method to Find the Area of an Irregular Shape?
We can decompose an irregular shape into regular polygons and then find the sum total of all the areas of the regular polygons to find the area of the irregular shape.
How Can We Find the Area of Irregular Shapes Using the Unit Square Method?
An irregular shape is divided into small squares of the unit square area. The total number of unit squares falling within the shape determines the total area. Count the square as “1” if the shaded region covers more than half while calculating the area for a more accurate estimate.
Is the Unit Square Method an Accurate Way to Find the Area of an Irregular Area?
While measuring the area of an irregular shape if we use the unit square method, we get the area as an accurate estimate. So in this case we get an approximate area of irregular shape instead of an accurate value of the area.