Let us see how it is.
Look at this circle. It’s radius is 5 cm.
Let us consider the circle is cut radially and started rearranging as shown below.
Let us see some more phases of continuity of rearranging.
Finally after complete rearrangement it takes a shape of rectangle as shown below.
Let us now see the dimensions of the rectangle.
The length = 5π units which is half of 10π units, the circumference of the circle.
The breadth = 5 units
Therefore we can conclude that area of circle = Area of rectangle = length × breadth = half of the circumference × radius = 5π × 5 = 25π square units
This is true for all dimensions of circle.
Click here for more detailed simulation.
Here, after rearrangement it can be noticed that circumference of the circle is shared equally to form the sides of rectangle length wise and the radius becomes the breadth of the rectangle.
Therefore Area of the circle = Area of rectangle = length × breadth = half of the circumference × radius = 𝜋r x r = πr2
Sujatha Karampuri, Teacher, Mathematics
Venu Gopal, Visiting Mathematics Mentor