# Area of Irregular Shapes

## Irregular shapes

Irregular shapes are polygons with five or more sides of varying lengths. These shapes or figures can be decomposed further into known shapes like triangles, squares, and quadrilaterals to evaluate the area.

Some examples of irregular shapes are as follows:

Daily Life Objects with Irregular Shapes ### How to Calculate the Area of Irregular Shape?

Finding the Area of Irregular Shapes

Different methods for estimating the area of irregular shape are:

• Evaluating area using unit squares.

• Dividing the irregular shape into two or more regular shapes.

• Dividing the irregular shape with curves into two or more regular shapes.

### How to Find the Area of an Uneven Shape?

Evaluating Area Using Unit Squares

We can use this method for shapes with curves apart from perfect circle or semicircles and irregular quadrilaterals. In this method, we first divide the shape into unit squares. The total number of unit squares falling within the shape is used to determine the total area. For example: Calculate the area by counting the unit squares in the given below figure. Ans: If we denote each unit square in centimetre, the area will be 6 cm2.

#### To Calculate the Area of an Irregular Shape with Curved Edges

Dividing the Irregular Shape Into Two or More Regular Shapes

Use this method to calculate the area of irregular shapes, which are a combination of triangles and polygons. Using predefined formulas calculate the area of such shapes and add them together to obtain the total area.

For example, in the given below irregular shape, we will divide multiple edges into a triangle and three polygons. The total area of the figure can be calculated by adding individual area:

Total Area = Area (ABIM) + Area (BCGH) + Area (CDEF) + Area (JKL)

⇒ Total area = (AB × BI) + (BC × CG) + (CD × DE) + (12 × LJ × KO)

⇒Total area = ( 10 × 5) + (3 × 3) + (2 × 2) + (1⁄2× 4 × 4)

⇒ Total area = 50 + 9 + 4 + 8

⇒ Total area = 71 cm2

### Calculating the Area of an Irregular Shape

To calculate the area of irregular shapes divide the shape with curves into two or more regular shapes.

In this method, divide an irregular shape into multiple squares, triangles, or other quadrilaterals. Depending on the shape or curves, a part of the figure can be a circle, semicircle or quadrant as well.

Find the are of a given irregular shape with 8 sides, including one curve.

Sol: We will determine the unknown quantities by the given dimensions for the sides. First, we need to divide the figure into two rectangles and a semicircle. The area of the shape ABCDEF is:

Total area (ABCDEF) = Area (ABCG) + Area (GDEF) + Area (aob)

Total area = (AB × AG) + (GD × DE) + (1⁄2 × π × ob2)

Total area = (3 × 4) + (10 × 4) + (1⁄2 × 3.14 × 12)

Total area = 12 + 40 + 1.57

Hence total area = 53.57 cm2

### How to Find the Area of Irregular Shapes Using Graph Paper?

What is the area of irregular surface?

Find the area of a given leaf. Solution: To find the area of the irregular surface in the above case leaf we have to put the leaf on graph paper and draw its boundary.  The shape of a leaf is irregular. So we will assume that more than half of the square covered by leaf will be counted as 1 and less than that will be counted as 0. Now count the number of fully covered shapes. There are 64 squares fully covered. Also, count the partially more than half covered squares and each will count qs 1 square. There are 17 square more than half square. Also, count the partially less than half covered square and each will count as 0. There are 16 squares less than half square.

Now add all the squares to find the area of leaf = 64 + 17 x 1 + 16 x 0 = 64 + 17 = 81 sq. units.

Hence the area of the leaf will be 81 sq. units.

### Area of Irregular Shapes Formula

To find the area of irregular shapes, first, we need to divide the irregular shape into regular shapes that you can recognize such as triangles, rectangles, circles, squares and so forth.

Then, find the area of these individual shapes and add them to get an area of irregular shapes.

### Solved Example

Q. Find the area of the given shape? Sol: The figure above has three regular shapes. Start dividing from the top, it has a triangle, a rectangle, and a trapezoid.

We will find the area for each of those three shapes and add the results to get the final area of a figure.

Triangle

Area of triangle = (base × height)/2

= (3 × 4)/2

= 12/2

= 6

Rectangle

Area of rectangle = length × width

= 3 × 10

= 30

Trapezoid

Area of trapezoid = ((b1 + b2) × h)/2

= ((3 + 5) × 2)/2

= (8) × 2/2

= 16/2

= 8

Hence area of the given shape = 6 + 30 + 8 = 44.