Page 170 - Ganit Kaushal

6.3 AREA OF PLANE FIGURES

The amount of the region enclosed by a closed curve (figure) is called its area.
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The units of area are square units. For example: mm , cm , m , km , etc.
Remember, some of the following conversions will be used frequently while solving problems related to area.
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1 m = 100 cm. So, 1 m × 1 m = 100 cm × 100 cm, or 1 m = 10,000 cm .
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Also, 1 cm = 10 mm. So, 1 cm × 1 cm = 10 mm × 10 mm, or 1 cm = 100 mm .
Finding Area with the Help of Formulae

We have the following formulas to find the area of a rectangle and a square.

Area of a rectangle = Length × Breadth

Area of a square = Side × Side = (Side) 2

Applications of Area in Daily Life

1. Carpeting a Room: If you want to buy carpet to cover your room’s floor, you need to know how
much surface area it has. You calculate the area of the floor.
2. Painting a Wall: To find out how much paint is needed to paint a wall, you first need to calculate
the area of the wall.
3. Growing Grass in a Lawn: If you want to grow grass in a rectangular lawn, you need to know
how much ground area will be covered. You need to find the area of the lawn.

Finding the Area of Regular Figures with the Help of a Square Grid Paper Sheet

Look at the adjoining figures, i.e., Fig. (i) and Fig. (ii).
Which one has a greater area?
We cannot answer the above question just by looking at these
figures. To find the answer, we place them on a square grid

paper sheet, where each square measures 1 unit × 1 unit = (i) (ii)
1 square unit.
Count the number of squares on a squared paper covered by each figure.

We see that the number of squares covered by Fig. (i) = 7.
So, the area of Fig. (i) = 7 sq. units.

Also, the number of squares covered by Fig. (ii) = 10.

So, the area of Fig. (ii) = 10 sq. units.
Now, we can say that figure (ii) has a greater area than figure (i), (i) (ii)
as 10 sq. units > 7 sq. units.

168 Mathematics-6