0Derive the formula for area of a circle if you are given area of triangle = (1/2) x (base) x (height) and circumference is 2 x π x radius.
Solution: Consider the below circle.
Consider that circle is madeup of concentric circles like the layers of an onion. We cut the circle on the dotted line and lay down the inner circles as well as the outermost circle, i.e. all the circles in a straight line then we get a triangle as shown below.
This is an isosceles traingle where the base is the circumference and the two sides are equal. We have the circumference of the circle and the area of the triangle. Therefore we can now say that Area of triangle = (1/2) x base x height, where height = radius, base = circumference.
Therefore Area = (1/2) x (r) x (2 x Π x r)
Area=Π x (r) x (r)
