Dear student Q1 For a polygon,radius=side2sin(180n)for hexagon with side aR=side2sin(180n)=a2sin(1806)=a2sin(30)=aRequired area=radius of circle-area of heaxagon=πR2-332a2=πR2-332R2 as R=a=2π-332R2 Regards

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Q1

F o r a p o l y g o n, r a d i u s = \frac{s i d e}{2 \sin (\frac{180}{n})} f o r h e x a g o n w i t h s i d e a R = \frac{s i d e}{2 s i n (\frac{180}{n})} = \frac{a}{2 s i n (\frac{180}{6})} = \frac{a}{2 s i n (30)} = a R e q u i r e d a r e a = r a d i u s o f c i r c l e - a r e a o f h e a x a g o n = {πR}^{2} - \frac{3 \sqrt{3}}{2} a^{2} = {πR}^{2} - \frac{3 \sqrt{3}}{2} R^{2} as R = a = (\frac{2 π - 3 \sqrt{3}}{2}) R^{2}

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