ГДЗ по геометрии 9 класс Мерзляк Задание 260

\[R = \ 2\ см.\]

\[1)\ a = 60{^\circ}:\]

\[S_{с} = \frac{a\pi R^{2}}{360{^\circ}} - \frac{1}{2}R^{2} \bullet \sin{60{^\circ}} =\]

\[= \frac{60{^\circ} \bullet \pi \bullet 4}{360{^\circ}} - \frac{4}{2} \bullet \frac{\sqrt{3}}{2} =\]

\[= \frac{2\pi}{3} - \sqrt{3} = \frac{2\pi - 3\sqrt{3}}{3}.\]

\[Ответ:\ \ \frac{2\pi - 3\sqrt{3}}{3}\ см^{2}.\]

\[2)\ a = 300{^\circ}:\]

\[S_{с} = \frac{a\pi R^{2}}{360{^\circ}} - \frac{1}{2}R^{2} \bullet \sin{300{^\circ}} =\]

\[= \frac{300{^\circ} \bullet \pi \bullet 4}{360{^\circ}} + \frac{4}{2} \bullet \frac{\sqrt{3}}{2} =\]

\[= \frac{10\pi}{3} + \sqrt{3} = \frac{10\pi + 3\sqrt{3}}{3}.\]

\[Ответ:\ \ \frac{10\pi + 3\sqrt{3}}{3}\ см^{2}.\]