In simple terms, we can say that a circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape in which the distance of all the points on the circle is same from it’s centre; this distance is also called radius of the circle. Few things around us that are circular in shape are bike wheels, a DVD and coins. We all know that the area of a circle is πr^2, but how? In this blog we’ll try to answer that question.
Let’s imagine taking a tomato and slicing it into 4 equal parts, now if we interlaced these parts as shown in the below image we’ll get a figure which barely resembles a rectangle.
But what if we take another tomato, slice it into 8 equal parts and interlaced them as shown in the below image? We’ll get a figure which somewhat more resembles a rectangle.
So if we divide the circle into even more smaller pieces, we can see that every time the shape becomes more like a rectangle.
But how small must we divide the circle before we get a perfect rectangle? It turns out that we can keep on dividing the circle into smaller and smaller pieces we can make but the answer is to divide the circle infinitely many times until we can’t distinguish the lines and eventually the circle can now become a perfect rectangle as shown below.
So, the area of the circle = area of rectangle = base x height
As we can see, the radius of the circle becomes the bases of the rectangle while the half of it’s circumference becomes the height of the rectangle.
Therefore, area of circle = r x 2πr/2, where 2πr is the circumference of the circle.
This gives us the area of circle to be πr^2.
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