For a circle with radius r
Area of circle will be
Area of circle = π r ^{ 2 }
Here,
π can be taken as
π = 3.14 or π = 22/7
Let’s take some examples
Find area of circle of radius 2 cm by counting squares (link), and also by formula
Covered Area 
Number 
Area 

1 
Fully  filled squares 
4 
1 × 4 = 4 
2 
Half  filled squares 
0 
1/2 × 0 = 0 
3 
More than Half  filled squares 
8 
1 × 8 = 8 
4 
Less than Half  filled squares 
4 
0 × 4 = 0 
Area = 4 + 0 + 8 + 0
= 12 cm ^{ 2 }
By formula of area of circle
Area = πr ^{ 2 }
= 3.14 × (2) ^{ 2 }
= 3.14 × 4
= 314/100 × 4
= 1256/100
= 12.56 cm ^{ 2 }
So, finding area by formula is more accurate
Find area of a circle with radius of 3.5 cm
Radius = r = 3.5 m
Area = πr ^{ 2 }
= π (3.5) ^{ 2 }
= 22/7 × (35/10) ^{ 2 }
= 22/7 × (7/2) ^{ 2 }
= 22/7 × 7/2 × 7/2
= 11/7 × 7/1 × 7/2
= 11/1 × 1 × 7/2
= 77/2
= 38.5 cm ^{ 2 }
∴ Area is 38.5 cm ^{ 2 }
Find area of a circle whose radius of 7 cm
Radius = r = 7 cm
Area = π r2
= 22/7 × (7)2
= 22/7 × 7 × 7
= 22 × 7
= 154 cm ^{ 2 }
^{ }
∴ Area is 154 cm ^{ 2 }
Find area of a circle with diameter 21 cm
Diameter = 21 cm
Radius = r = Diameter/2
= 21/2 cm
Now,
Area = π r ^{ 2 }
= 22/7 × (21/2) ^{ 2 }
= 22/7 × 21/2 × 21/2
= 11/7 × 21/1 × 21/2
= 11/1 × 3 × 21/2
= (33 × 21)/2
= 693/2
= 346.5 cm ^{ 2 }
∴ Area is 346.5 cm ^{ 2 }
Find area of a circle with diameter 42 cm
Diameter = 42 cm
Radius = r = Diameter/2
= 42/2 cm
= 21 cm
Now,
Area = π r ^{ 2 }
= 22/7 × (21) ^{ 2 }
= 22/7 × 21 × 21
= 22/1 × 3 × 21
= 66 × 21
= 1386 cm ^{ 2 }
∴ Area is 1386 cm ^{ 2 }
Find area of a circle with radius 5 cm
Radius = r
= 5 cm
Now,
Area = π r ^{ 2 }
= 3.14 × (5) ^{ 2 }
= 3.14 × 25
= 314/100 × 25
= 314/20 × 5
= 314/4 × 1
= 157/2
= 78.5 cm ^{ 2 }
∴ Area is 78.5 cm ^{ 2 }
Find the area of a circle with diameter 30 cm
Diameter = 30 cm
Radius = r = Diameter/2
= 30/2 cm
= 15 cm
Now,
Area = π r ^{ 2 }
= 3.14 × (21) ^{ 2 }
= 3.14 × 225
= 314/100 × 225
= 314/20 × 45
= 157/10 × 45
= 7065/10
= 706.5 cm ^{ 2 }
∴ Area = 706.5 cm ^{ 2 }