Formula for the area of a rectangle. , Formula for the area of a square., Example and solution for area of a rectangle, area of a square.

__Area of the rectangle and square__

** **

**Situation**

There
are lot of mosquitoes in Kavitha's house. These mosquitoes enter her house
through the windows. Kavitha's mother decided to cover the windows by a mesh.
What kind of measurement is required by Kavitha's mother to cover the window
using the mesh?

The
measurement required by Kavitha's mother to cover the window is the area.

Area
can be defined as the space occupied by a flat shape or the surface of an
object.

The
unit denoted for the area of an object is square units. (Example: 16 sq. cm, 24
sq. m).

__Formula for the area of a rectangle__

**Formulas**

Area of the rectangle =* l *×
*b*

Area of the square = a^{2}

In the rectangle ABCD given above, 1 cm
divisions were marked on each side.

The points on opposite sides were
joined as shown in the figure above. The length of the sides of each square
thus created is 1 cm.

Therefore, the area of each square is
1 sq.cm, which is the unit square.

In the rectangle ABCD we have created
2 rows of 6 squares each.

Therefore, the number of squares in
the rectangle ABCD is 6 × 2 = 12

Here, the length of the rectangle ABCD
is 6 cm and its breadth is 2 cm.

The number of unit squares formed are
the same as the product of the length and breadth of the rectangle.

Therefore, the area of rectangle ABCD
= 6 × 2 = 12 sq.cm

Therefore, the **area of the rectangle = length × breadth**

__Formula for the area of a
square:__

In the square ABCD given above, 1 cm
divisions were marked on each side.

The points on opposite sides were
joined as shown in the figure above. In the square ABCD we have created 4
rows of 4 squares each. The length of the sides of each square thus created is
1 cm.

Therefore, the area of each square is
1 sq.cm, which is the unit square.

Look at the square given above. The
side of the square is 4 cm and we have 16 squares of 1cm each within this
square.

The number of unit squares formed are
the same as the product of two sides of the square.

Since the length of each side of the
square is 4 cm the area of the square = 4 × 4 = 16 sq.cm.

Therefore, the **area of a square = length of a side × length of a side**

It is not necessary to divide a square
or rectangle into small squares every time when you calculate their area. The
advantage of a formula is that you can calculate the area simply by
substituting the appropriate values.

__Example
1.5__

What
is the area of a rectangle of length 10 cm and breadth 8 cm?

**Solution**

Area
of a rectangle = length × breadth

= 10 × 8

= 80

Therefore,
the area of the rectangle is 80 sq.cm.

** **

__Example
1.6__

A
wall that is 6 m long and 2 m wide has to be painted. If the labour charges are
₹ 20 per sq.m, then what is the cost of labour for painting the wall?

**Solution**

First
let us calculate the area of the wall to be painted

Area
of the wall = length of the wall × breadth of the wall

=
6 × 2 = 12

Thus,
the area of the wall is 12 sq.m.

Labour
cost of 1 sq.m is ₹ 20.

So,
the labour cost for 12 sq.m. = 12 × 20 = ₹ 240.

Therefore,
the cost of labour for painting the wall is ₹ 240.

__Example
1.7__

What
is the area of a square with side 12 cm?

**Solution**

Area
of a square = length of a side × length of a side

=
12 × 12 = 144

Therefore,
the area of the square is 144 sq.cm.

__Example
1.8__

One
side of a square room is 3 m. If the cost of labour for laying 1 sq.m of the
floor is ₹ 25, then what is the total cost of labour?

**Solution**

First
we must find the area of the square room

Area
of the square room = length of a side × length of a side

=
3 × 3 = 9

Therefore,
the area of the square room is 9 sq. m.

The
labour cost of laying 1 sq.m of flooring is ₹25.

Therefore,
the cost of laying 9 sq.m of flooring is 25 × 9 = ₹ 225.

Tags : Geometry | Term 3 Chapter 1 | 5th Maths , 5th Maths : Term 3 Unit 1 : Geometry

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5th Maths : Term 3 Unit 1 : Geometry : Area of the rectangle and square | Geometry | Term 3 Chapter 1 | 5th Maths

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