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Question Number 20944 by tawa tawa last updated on 08/Sep/17

Answered by dioph last updated on 09/Sep/17

Commented by dioph last updated on 09/Sep/17

$$r\frac{\sqrt{3}}{2}=7\sqrt{3}\Rightarrow r=14\mathrm{cm}$$$$A=4\times \left(\frac{\pi r^2}{6}\right)-2\times \left(\frac{r^2\sqrt{3}}{4}\right)$$$$=4\times \left(\frac{22\times {14}^2}{7\times 6}\right)-2\times \left(\frac{{14}^2\times \sqrt{3}}{4}\right)$$$$=\frac{1232}{3}-98\sqrt{3}$$$$=(411-\frac{1}{3})-\sqrt{28812}$$$$\mathrm{But}\sqrt{28900}=170,\mathrm{and}$$$${(170-\frac{1}{3})}^2={170}^2-\frac{340}{3}+\frac{1}{9}<{170}^2-113=27787$$$$\mathrm{Hence}(170-\frac{1}{3})<\sqrt{28812}<170$$$$\Rightarrow 241-\frac{1}{3}<A<241$$$$\mathrm{So}A=241{\mathrm{cm}}^2\mathrm{to}\mathrm{the}\mathrm{nearest}{\mathrm{cm}}^2$$

Commented by tawa tawa last updated on 10/Sep/17

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

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