Areas of Irregular Figures

Areas of irregular figures can be determined by dividing the figure into squares and rectangles.

Some irregular figures are made of rectangular or square regions. The areas of such irregular figures can be determined by calculating the areas of these rectangles and squares.

To find the area of a figure which is a combination of rectangles and a squares, we calculate the area of each figure separately and then add them to find total area.

Solved examples to find areas of irregular figures:

1. Find the area of the given figure:

Areas of Irregular Figures

Solution:

Area of a rectangle ABDC = 3 × 1 

                                     = 3 sq. cm.

Area of a rectangle EFGD = 2 × 1

                                     = 2 sq. cm.

Therefore, Total Area = 3 + 2

                               = 5 sq. cm.

Area of the given figure = 5 sq. cm.


2. Find the area of the following figures.

Area of Combined Figures

Solution: 

Area of the rectangle PQTU = 5 × 3 = 15 sq. cm.

Area of the square VRST = 2 × 2 = 4 sq. cm.

Total area of the figure = 15 + 4 = 19 sq. cm.


3. Find the area of the following figure.

Area of Irregular Shapes

Total area = Area of the rectangle ABGF + Area of the rectangle CDEG

               = 8 × 2 cm\(^{2}\) + 2 × (8 - 2) cm\(^{2}\)

               = 16 sq cm\(^{2}\) + 2 × 6 cm\(^{2}\)                

               = (16 + 12) cm\(^{2}\)

               = 28 cm\(^{2}\)

Therefore, area of the figure = 28 cm\(^{2}\)


4. Find the area of the following figure.

Area of Irregular Figures

(i) We divide the figure into two parts.

PQRS is a rectangle of length 9 cm and breadth 5 cm.

Area of PQRS = 9 × 5

                    = 45 sq. cm

STUV is a square of side 3 cm

Area of square STUV = 3 × 3 = 9 sq. cm

Hence, total area of the figure = 45 + 9 = 54 sq. cm


5. Find the area of the figure given on the right side.

Irregular Shapes Area

Total area = Area of the rectangle ABKL + Area of the rectangle EFGH + Area of the rectangle CDIJ

                = 20 × 4 cm\(^{2}\) + 20 × 4 cm\(^{2}\) + 8 × 4 cm\(^{2}\)

                = 80 cm\(^{2}\) + 80 cm\(^{2}\) + 32 cm\(^{2}\)

                = (80 + 80 + 32) cm\(^{2}\)

                = 192 cm\(^{2}\)

Therefore, area of the figure = 192 cm\(^{2}\)


6. Find the area of the following figure.

Area of Composite Figures

Figure QTUV is a rectangle of length (5 cm + 5 cm = 10 cm) and breadth 2 cm

Area of QTUV = 10 × 2

                    = 20 sq. cm

PQRS is a square of side 5 cm

Area of PQRS = 5 × 5 = 25 sq. cm

Hence, total area of the figure = 20 + 25

                                            = 45 sq. cm

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