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Question-115237




Question Number 115237 by nisaketto last updated on 24/Sep/20
Answered by nimnim last updated on 24/Sep/20
A=area of regular hexagon−area of circle      =((3(√3))/2)a^2 −πr^2 =(((3×1.732)/2)×6×6)−(((22)/7)×2×2)      =93.528−0.785=92.77cm^2     the question said radius is 2cm while the    figure represent radius is 4.2cm  OR ( ((3(√3))/2)×6×6)−(((22)/7)×4.2×4.2)      =93.528−55.55      =38.088≈38.09 cm^2
$$\mathrm{A}=\mathrm{area}\:\mathrm{of}\:\mathrm{regular}\:\mathrm{hexagon}−\mathrm{area}\:\mathrm{of}\:\mathrm{circle} \\ $$$$\:\:\:\:=\frac{\mathrm{3}\sqrt{\mathrm{3}}}{\mathrm{2}}\mathrm{a}^{\mathrm{2}} −\pi\mathrm{r}^{\mathrm{2}} =\left(\frac{\mathrm{3}×\mathrm{1}.\mathrm{732}}{\mathrm{2}}×\mathrm{6}×\mathrm{6}\right)−\left(\frac{\mathrm{22}}{\mathrm{7}}×\mathrm{2}×\mathrm{2}\right) \\ $$$$\:\:\:\:=\mathrm{93}.\mathrm{528}−\mathrm{0}.\mathrm{785}=\mathrm{92}.\mathrm{77cm}^{\mathrm{2}} \\ $$$$\:\:{the}\:{question}\:{said}\:{radius}\:{is}\:\mathrm{2}{cm}\:{while}\:{the} \\ $$$$\:\:{figure}\:{represent}\:{radius}\:{is}\:\mathrm{4}.\mathrm{2}{cm} \\ $$$${OR}\:\left(\:\frac{\mathrm{3}\sqrt{\mathrm{3}}}{\mathrm{2}}×\mathrm{6}×\mathrm{6}\right)−\left(\frac{\mathrm{22}}{\mathrm{7}}×\mathrm{4}.\mathrm{2}×\mathrm{4}.\mathrm{2}\right) \\ $$$$\:\:\:\:=\mathrm{93}.\mathrm{528}−\mathrm{55}.\mathrm{55} \\ $$$$\:\:\:\:=\mathrm{38}.\mathrm{088}\approx\mathrm{38}.\mathrm{09}\:\mathrm{cm}^{\mathrm{2}} \\ $$
Answered by EvoneAkashi last updated on 24/Sep/20
The area of the hexagon is ((3(√3))/2)×6^2 =54(√3)cm^2 .  The area of the circle is π×2^2 =4πcm^2 ,  So the area finded is (54(√3)−4π)cm^2 .
$${The}\:{area}\:{of}\:{the}\:{hexagon}\:{is}\:\frac{\mathrm{3}\sqrt{\mathrm{3}}}{\mathrm{2}}×\mathrm{6}^{\mathrm{2}} =\mathrm{54}\sqrt{\mathrm{3}}{cm}^{\mathrm{2}} . \\ $$$${The}\:{area}\:{of}\:{the}\:{circle}\:{is}\:\pi×\mathrm{2}^{\mathrm{2}} =\mathrm{4}\pi{cm}^{\mathrm{2}} , \\ $$$${So}\:{the}\:{area}\:{finded}\:{is}\:\left(\mathrm{54}\sqrt{\mathrm{3}}−\mathrm{4}\pi\right){cm}^{\mathrm{2}} . \\ $$

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