The area is a measure of how much space there is on a flat surface.

__Area:__

The area is a measure of how much
space there is on a flat surface.

The area of the plot of land is
derived by multiplying the length and breadth

Area = length × breadth

The unit of the area is = metre ×
metre

= metre^{2}

= m^{2} ( Read as square metre)

Area is a derived quantity as we
obtain are by multiplying twice of the fundamental physical quantity length.

One square metre is the area enclosed inside a square of
side 1 metre.

**Problem 1.1**

What is the area of a 10 squares
each of side of 1 m.

Area of a square = side × side

=1 m × 1 m

=1 m^{2}
or 1 square metre

Area of 10 squares = 1 square metre
× 10

= 10 square
metre

(Even though the area is given in
square metre , the surface need not to be square in shape)

**Area of regularly shaped figures**

The area of regularly shaped figures
can be calculated using the relevant formulae. In the table 1.2, the formulae
used to calculate the area of certain regularly shaped figures are given.

**Problem 1.2**

Find the area of the following
regular shaped figures: (Take π = 22/7)

a.
A rectangle whose
length is 12 m and breadth is 4 m.

b. A circle whose radius is 7 m.

c. A triangle whose base is 6 m and
height is 8 m.

**Solution:**

(a) Area of rectangle = length ×
breadth

= 12×4

= 48 m^{2}

(b) Area of circle= π × r^{2}
= (22/7) × 7 × 7

= 154 m^{2}

(c) Area of triangle = (1/2) × base
× height

= (1/2) × 6 × 8

= 24 m^{2}

**Table 1.2 Area of some regularly shaped figures**

**Area of irregularly shaped figures**

In our daily life, we encounter many irregularly shaped figures like leaves, maps, stickers of stars or flowers, peacock feather etc. The area of such irregularly shaped figures cannot be calculated using any formula.

How can we find the area of these
irregularly shaped objects?

We can find the area of these
figures with the help of a graph sheet.

The following activity shows how to
find the area of irregularly shaped plane figures.

*The graphical method explained above
can be used to find the area of regularly shaped figures also. In the case of
square and rectangle, this method gives the area accurately.*

**ACTIVITY 1**

Take a leaf from any one of trees in your neighbourhood.
Place the leaf on a graph sheet and draw the outline of the leaf with a pencil
(Figure 1.2). Remove the leaf. You can see the outline of the leaf on the graph
sheet.

**Figure 1.1**
Area of an irregularly shaped plane figure

i. Now, count the number of whole squares enclosed within
the outline of the leaf. Take it to be M.

ii. Then, count the number of squares that are more than
half. Take it as N.

iii. Next, count the number of squares which are half of a whole square. Note it to be

P. Finally, count the number of squares that are
less than half. Let it be Q.

v. M = __ 51 __; N = __ 15 __; P = __4__; Q = __11__

Now, the approximate area of the leaf can be calculated
using the following formula:

Approximate area of the leaf = M + (3/4) N + (1/2) P + (1/4) Q square cm.

Area of the leaf = ** 51+ (¾) × 15 + (½) × 4 + (¼) × 11**.

__= 51 + 11.25 + 2 + 2.75 = 67 square cm. __

This formula can be used to calculate the area of any
irregularly shaped plane figures.

Tags : Measurement | Term 1 Unit 1 | 7th Science , 7th Science : Term 1 Unit 1 : Measurement

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7th Science : Term 1 Unit 1 : Measurement : Area | Measurement | Term 1 Unit 1 | 7th Science

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