$$S=\frac{1}{2}R^2n\sin \frac{360^\circ}{n},$$ $$R=\frac{a}{2\sin \frac{180^\circ}{n}},\;\;r=\frac{a}{2\text{tg } \frac{180^\circ}{n}}.$$

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Вид правильного многоугольника	$$\alpha$$	$$R$$	$$r$$	Сумма углов
	$$60^\circ$$	$$\frac{a\sqrt 3}{3}$$	$$\frac{a\sqrt 3}{6}$$	$$180^\circ$$
	$$90^\circ$$	$$\frac{a\sqrt 2}{2}$$	$$\frac{a}{2}$$	$$360^\circ$$
	$$120^\circ$$	$$a$$	$$\frac{a\sqrt 3}{2}$$	$$720^\circ$$

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