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Triangle Proof – The formula for the area of a circle is half the circumference multiplied by the radius. The area of a circle can be described as the area of a triangle with the height equal to the radius and the base length equal to the circumference. The area of a triangle is equal to half the base × the height.
The circumference is equal to Pi(π) × Diameter. Half of the circumference can be thought of as Pi(π) × Radius. So the formula can be shortened to π × r × r or πr^{2};

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