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Question
In fig. 3, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 20 cm, find the area of the shaded region. (Use π = 3.14)
Solution
Let us join OB.
In ΔOAB:
OB2 = OA2 + AB2 = (20)2 + (20)2 = 2 × (20)2
⇒ OB = 20 √2
Radius of the circle, r = `20 sqrt2` cm
`"Area of qudrant OBPQ"=90^@/360^@xx3.14xx(20sqrt2)^2`
`=90/360xx3.14xx(20sqrt2)^2 cm^2`
`=1/4xx3.14xx800 cm^2`
`=628 cm^2`
Area of square OABC = (Side)2 = (20)2 cm2 = 400 cm2
∴ Area of the shaded region = Area of quadrant OPBQ − Area of square OA
= (628 − 400) cm2
= 228 cm2
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