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Question

In the figure, ODCE is a square then the area of shaded region is
241895_4867fe3987124031b288efea05413022.png

A
52.5cm2
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B
24.5cm2
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C
49cm2
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D
None of these
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Solution

The correct option is A 52.5cm2
GivenODCEisasquareofside=7cm.ACBisanarcwithOascentreandthepointsA&BlieonODextendedandOEextended.TofindoutTheareaoftheshadedregionACBED.SolutionThearcACBpassesthroughCandthecentreisatO.Itsradius=r=diagonalOCofthesquare.NowODCEisasquareofside=7cm..ThediagonalOC=side×2=72cm.r=72cm.AlsoAOB=θ=90o.ar.sectorAOB=θ360o×π×r2=90o360o×227×(72)2cm2=14×227×98cm2=77cm2.Againar.ΔEOD=12×base×height=12×OD×OE=12×7×7cm2=492cm2=24.5cm2.Nowar.ACBD=ar.sectorAOBar.ΔEOD=(7724.5)cm2=52.5cm2.Soar.shadedregion=52.5cm2.AnsOptionA.

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