Proof That For All Circles The Area Is Half The Product Of The Circumference And The Radius

Here is a proof that, for all circles, the area is half of the product of the circumference and the radius:

• Circles can be divided into congruent sectors:
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• The sectors can be rearranged:
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• As the number of sectors increases, the shape approaches a rectangle:
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• Therefore, the area is half of the product of the circumference and the radius for all circles.
• QED