If the radius of the circle is r, then the area of the circle is πr ^ 2. we can find the area by putting the value of r. so easy, isn’t it. But a question? Well, how is the area of the circle (πr ^ 2)? Have you ever thought of that?

People who know integration might say, “yes, I did.” But what happened to them who don’t know integration. Yeap today's article is for them who don’t know integration and how we get the area of circle πr^2.

Let's start with a sharp knife which we will use for cutting. Fear not, we will not cut anything else, we will cut a circle. Why cut? Follow me, you’ll learn.

First, we cut I mean divide the circle into 8 equal parts. It's not mandatory to cut the circle into 8 parts. I divided it into 8 parts. If you want, you can divide it into 10 parts or divide it into 100 parts. Now I will try to make a rectangle by arranging these 8 parts.

Uhm no! It's not the rectangle, why? Because it has become crooked. Well, don't worry, we share more and more. Well, how much will I share? 100 time? At 1000 times? At 10,000 times? Yes, the more equal parts you divide, the more perfect rectangles you will get. But how much more will you share?

When can I cut as my desire then why cut a little? We will cut the circle in an infinity number. Dividing it an infinite time, the dividing lines can no longer be separated. After that, a perfect rectangle can be found by arranging those parts. So what do we mean by this? We understand that the area of a circle will be equal to the area of this rectangle.

And we know,

Area of rectangle = land x height.

Well, what will be the value of the land in this rectangle? Can anyone remember that? It will be the length of the ground of the rectangle will be half the circumference of the circle. And what will be the height of the rectangle? The height will be equal to the radius of the circle. So Height = r. Well, what is the value of the circumference of the circle? 2πr

However, the land of the rectangle = 2πr / 2 = πr

So what is the area of that rectangle?

Area = πr (Land) x r (Height) = πr ^ 2

So the area of the circle is = the area of the rectangle = πr ^ 2.