Area of a Circle : Something I never learned at school

I was taught how to find area of a circle when in school. The teacher wrote down the formulae on the blackboard and I accepted it as absolute truth.

Later in my life I used integral calculas to derive the formulae for the area of a circle, but I never found a way to explain it to a 11 year old, till recently.

At my son’s primary school , the maths teacher explained why the area of a circle is pr² by cutting a pair of cardboard discs. Apparently it was first derived by Archimedes. I was amazed at the beauty and the simplicity of the proof . Why didn’t they teach it in our schools ?

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So we need to show that the area of a circle = pr² , where r = radius and p is the ratio of circumference and diameter of the circle.

Diameter d=2r

Now…