What will be the area of shaded region (grey colored) if the given figure is square of side 6cm?

enter image source here

1 Answer
CW
Jul 30, 2017

shaded area =6*(3sqrt3-pi) ~~ 12.33 " cm"^2=6⋅(3√3−π)≈12.33 cm2

Explanation:

enter image source here
See the figure above.

Green area ==area of sector DAFDAF - yellow area

As CF and DFCFandDF are the radius of the quadrants,
=> CF=DF=BC=CD=6⇒CF=DF=BC=CD=6
=> DeltaDFC is equilateral.
=> angleCDF=60^@
=> angleADF=30^@
=> EF=6sin60=6*sqrt3/2=3sqrt3

Yellow area = area of sector CDF- area DeltaCDF
= pi*6^2*60/360-1/2*3sqrt3*6
= 6pi-9sqrt3

Green area = =area of sector DAF - yellow area
=pi*6^2*30/360-(6pi-9sqrt3)
= 3pi-(6pi-9sqrt3)
= 9sqrt3-3pi

Hence, the shaded area A_s in your figure = 2xx green area
=> A_s=2*(9sqrt3-3pi)
=18sqrt3-6pi=6(3sqrt3-pi)~~12.33 " cm" ^2

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