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Rectangle 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 rectangle with one side length equal to the radius and the other as half of the circumference. 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};