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Question
In Fig. 6, OABC is a square of side 7 cm. If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region. `[\text\ User=22/7]`
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Solution
It is given that OABC is a square of side 7 cm.
∴ Area of square OABC = (7)2 cm2 = 49 cm2
Also, it is given that OAPC is a quadrant of circle with centre O.
∴Radius of the quadrant of the circle = OA = 7 cm
∴ Area of the quadrant of circle `1/4(pi^2)`
`=1/4(pixx7^2)cm^2`
`=(49pi)/4cm^2`
`=49/4xx22/7 cm^2`
`=77/2cm^2`
∴Area of the shaded region = Area of Square − Area of Quadrant of circle.
`=[49-77/2]cm^2`
`=[(98-77)/2]cm^2`
`=21/2cm^2`
`=10.5cm^2`
Thus, the area of the shaded region is 10.5 cm2.
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