Explain the derivation of area of circle

2
by malek

2016-03-04T14:23:48+05:30
Formula for area of the circle = pi*r*r=pi*r^2
pi = 3.14 or 22/7
r = radius of the circle
2016-03-05T00:45:17+05:30

The polygon can be broken down into n isosceles triangles (wheren is the number of sides), such as the one shown on the right.

In this triangle
s   is the side length of the polygon
r   is the radius of the polygon and the circle
h   is the height of the triangle.

The area of the triangle is half the base times height orThere are n triangles in the polygon soThis can be rearranged to beThe term ns is the perimeter of the polygon (length of a side, times the number of sides). As the polygon gets to look more and more like a circle, this value approaches the circle circumference, which is 2πr. So, substituting 2πr for ns:Also, as the number of sides increases, the triangle gets narrower and narrower, and so when s approaches zero, h and r become the same length. So substituting r for h:Rearranging this, we get