# Area of Irregular Shapes – Definition with Examples

## Area of Irregular Shapes

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

Some examples of irregular shapes are as follows:

Daily life objects with irregular shapes

Calculating the area of irregular shapes:

The approaches to estimating the area of irregular shape are:

Evaluating area using unit squares

Apply this technique for the shapes with curves apart from perfect circle or semicircles and irregular quadrilaterals. In this method, divide the shape into unit squares. The total number of unit squares falling within the shape determines the total area.

Figure: Some examples of irregular shapes

Count the square as “1” if the shaded region covers more than half while calculating the area for a more accurate estimate.

Figure: For the irregular shape, count the squares with orange and yellow coding as 1.

In the following figure, calculate the area by counting the unit squares, which is 6. If we denote each unit square in centimeter, the area will be 6 cm2.

Figure: Calculating the area of an irregular shape with curved edges

• Dividing the irregular shape in two or more regular shapes

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

For example, an irregular shape we divide multiple edges into a triangle and three polygons.

The total area of the figure is given as:

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

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

⇒ Area = ( 10 × 5) + (3 × 3) + (2 × 2) + (12× 4 × 4)

⇒ Area = 50 + 9 + 4 + 8

⇒ Area = 71 cm2

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

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

The following figure is an irregular shape with 8 sides, including one curve. Determine the unknown quantities by the given dimensions for the sides. Decompose the figure into two rectangles and a semicircle.

The area of the shape ABCDEF is:

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

Area = (AB × AG) + (GD × DE) + (12 × π × ob2)

Area = (3 × 4) + (10 × 4) + (12 × 3.14 × 12)

Area = 12 + 40 + 1.57

Area = 53.57 cm2

Application

The estimation of area for irregular figures is an essential method for drawing maps, building architecture, and marking agricultural fields. We apply the concept in the cutting of fabrics as per the given design. In higher grades, the technique lays a basis for advanced topics such as calculating volume, drawing conic sections and figures with elliptical shapes.

• Square
• Rectangle
• Triangle
• Circle
• Area
• Irregular and regular shapes

## Practice Problems

1

### A leaf was traced on a graph paper. It has 10 squares fully covered, 12 squares are covered more than half and 14 squares are covered less than half. What will be the area of the leaf?

29 square units
16 square units
22 square units
23 square units
CorrectIncorrect
Correct answer is: 22 square units
The fully covered squares are counted as it is. More than half-covered squares are counted as 1 square each. Less than half-covered squares are counted as 0 each.
So we have $10 + (1 × 12) + (0 × 14) = 10 + 12 = 22$ square units.
2

### What is the area of a field that is shaped like 2 rectangles with the following measurements: Rectangle 1: l = 5, w = 6 Rectangle 2: l = 8, w = 5

48 square cm
24 square cm
70 square cm
10 square cm
CorrectIncorrect
Correct answer is: 70 square cm
Area of Rectangle 1 = 5 × 6 = 30 sq.cm.
Area of Rectangle 2 = 8 × 5 = 40 sq.cm
Area of Field = Area of Rectangle 1 + Area of Rectangle 2
= 30 + 40 = 70 square cm.
3

### To find the area of an irregular shape, we first break the irregular shape into common shapes. Then we find the area of each shape and ___ them.

Multiply
Subtract
Divide
CorrectIncorrect
To find the area of an irregular shape, we first break the shape into common shapes. Then we find the area of each shape and add them. For example, if an irregular polygon is made up of a square and a triangle, then: Area of irregular polygon = Area of Square + Area of Triangle.
4

### What is the area of an irregular polygon made of 2 squares with the following measurements? Square 1: side = 5 cm Square 2: side = 3 cm

25 square cm
34 square cm
9 square cm
16 square cm
CorrectIncorrect
Correct answer is: 34 square cm
Area of Square 1 = 5 × 5 = 25 sq. cm.
Area of Square 2 = 3 × 3 = 9 sq. cm.
Area of Irregular polygon = Area of Square 1 + Area of Square 2 = 25 + 9 = 34 square cm.