This document provides information about calculating the area of a circle. It defines a circle and key terms like radius, diameter, chord, and circumference. It then derives the formula for the area of a circle as A = πr^2 by dividing a circle into sectors and arranging them to form a rectangle. Some examples are provided to demonstrate calculating the area given the radius or circumference. The document concludes by stating the area formula can be used to find the area of circular objects and shapes in daily life.

1. ‫عليكم‬ ‫السالم‬..........‫سامى‬ ‫عماد‬ ‫مستر‬ ‫معكم‬Area of the circle

2. Q . What is the shape of these things?
A . All the things are having circular shapes.

3. Q . What is the shape of this stadium?
A .The shape of this stadium is circular.

4. Here is a circular garden and we want to find the l
cost of planting grass in it, which thing we need to
measure ?
Area of circular garden.

5. AREA OF A
CIRCLE
 Definition
 Important Terms
 Derivation of Formula
 Related Examples
 Daily Life Applications of Circle

6. Definition
The locus of points whose distance from a fixed point is
always constant.
The fixed point is called centre and is denoted by ‘O’.

7. Q
AREA OF A CIRCLE
Important Terms
Radius
The distance of any point on the circle from the
centre is called radius. It is denoted by ‘r’. OA is the
radius of the circle.
P
Chord
A line segment having end
points on the circle. In figure the
line segment PQ is the chord of the
circle.
O
r
A
.

8. AREA OF A CIRCLE
Important Terms
Diameter
A chord through the centre of a circle is called
diameter of the circle. The line segment PC is the diameter
O
. CP
Arc
The distance between two
points on the boundary of circle
is called an arc. e.g. CD is an arc.
D

9. 7
and  = 22
= 3.1416 approximately.
AREA OF A CIRCLE
Important Terms
Circumference
The distance around a circle is called the
circumference. The ratio of circumference of a circle to its
diameter is constant and is denoted by a Greek letter  (pi)

10. by
Where is the ratio between circumference
and diameter of a circle.
A  π r2

AREA OF ACIRCLE
Derivation of Formula
The measure of plane region bounded by a circle
is called its area. The area of a circle of radius r is given

11. Derivation of Formula
 Consider a circle of radius r
 Divide this circle into even number of equal parts
.o r

12. .
o r
2
8
6
5 4
1
7
3
AREA OF A CIRCLE
Derivation of Formula
Let us divide the circle into eight equal parts

13. .
o r
2
8
6
5 4
1
7
3
3
21
654
87
AREA OF A CIRCLE
Derivation of Formula
Join these parts to form a parallelogram

14. Q. What is the circumference of a circle?
.
o r
2
8
6
5 4
1
7
3
Derivation of Formula
C =  r C = 2  r C =  r2C = 2  r

15. Q. What is the area of a parallelogram?
.
o r
2
8
6
5 4
1
7
3
AREA OF A
CIRCLE
x
Width x Width Length x Length Length x WidthLength x Width

16. Area of parallelogram = length x Width
Area of parallelogram = r x r = r2
.
o r
2
8
6
5 4
1
7
3
AREA OF A CIRCLE
Derivation of Formula
x

17. Hence area of circle = A  π r2
.
o r
2
8
6
5 4
1
7
3
AREA OF A CIRCLE
x

18. We can divided the circle into
a lot of sectors
arrange them like this
we will discover a rectangle
the area of rectangle = length×width
the area of the circle = 𝜋𝑟2
x
x

19. EXAMPLES

20. AREA OF A CIRCLE
What is the area of circle whose radius is 3 cm .
Solution: area of the circle = π r2
2
3.14 × 𝟑
= ………..

21. Circle M is drawn inside a square of
side length 14 cm and touched its
sides .
Calculate the area of the coloured
part
consider  =
𝟐𝟐
𝟕

22. To find the area of coloured part
we should first find
the area of the square = side
length × side length
14 × 14 = 196 c𝑚2
area of the circle = π r2
=
𝟐𝟐
𝟕
×72
= 154 c𝑚2
area of coloured part = 196 – 154 =42 c𝑚2

23. Find the area of each of the
following ( =
𝟐𝟐
𝟕
)

24. A circle of circumference is
62.8 cm . Calculate its area
( = 3.14 )

25. Solution
area of the circle = π r2
circumference of the circle
= π d
d =
𝒄
π
62.8
3.14
= 20 cm
r = 10 cm
A = π r2 3.14 × 100
= 314 c𝑚2

26. MREMADSAMY
Thankyou