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प्रश्न
In the given figure, a square OABC has been inscribed in the quadrant OPBQ. If OA = 20 cm, then the area of the shaded region is
पर्याय
214 cm2
228 cm2
242 cm2
248 cm2
उत्तर
228 cm2
Join OB.
Now, OB is the radius of the circle.
We have :
OB2 = OA + AB [By pythagoras' therom]
⇒ OB2 = {(20)2 + (20)2} cm2
⇒ OB2 =(400+400) cm2
⇒ OB2 = 800 cm2
`=> "OB" =20sqrt2 "cm"`
Hence, the radius of the circle is `20sqrt(2) "cm".`
Now,
Area of the shaded region = Area of the quadrant - Area of the square OABC\
`=|(1/4xx3.14xx20sqrt(2)xx20sqrt(2))-(20xx20)| "cm"^2`
`=|(1/4xx314/100xx800)-400| "cm"^2`
=(628-400) cm2
= 228 cm2
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