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Area of a circle = pi x r2. So how did the ancients ever know this without using calculus? Simple. They changed the circle into a triangle or rectangle, enabling them to find the area.
The illustration below shows how to convert the circle into a triangle with the same area (top), or how to form a rectangle with the same area (bottom).
Pi = circumference/diameter = circumference/2 x radius = approximately 22/7
I include two graphics below showing another way to convert a circle to a triangle, and to derive the formula for the area of a circle. By the way, C = circumference = pi x diameter = pi x (2 x radius)
copyright 2012 by Bruce McClure
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