Calculate the area of the shaded region? This question please about radians, i would appreciate your help

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Answer 1 · 2016-11-26T16:27:25

Area of shaded region is $8.876$ $cm^2$

If we join $OA$ , $DeltaOAB$ is right angled triangle at $/_B$ and $/_BOA=pi/3=60^o$ and $/_BAO=pi/6=30^o$

hence $BA=3.6xxsqrt3$ $cm.$

and as area of a right triangle is half the product of its legs forming right angle,

area of $DeltaOAB=(3.6xx3.6xxsqrt3)/2=3.24xxsqrt3=11.224$ $cm^2$

Hence area of quadrilateral is $2xx11.224=22.448$ $cm^2$

Now area of sector (this is one-third of circle of radius $3.6$ $cm,$ )
is

$1/3xxpixx3.6xx3.6=3.1416xx1.2xx3.6=13.572$ $cm^2$

Hence area of shaded region is $22.448-13.572=8.876$ $cm^2$ .