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Question
In the following figure, OE = 20 cm. In sector OSFT, square OEFG is inscribed. Find the area of the shaded region.
Solution
We have to find the area of the shaded portion. We have, `OE=20cm`and OEFG is a square.
Use Pythagoras theorem to find OF as,
`OF=(sqrt((20)^2+(20)^2))cm`
`= 20sqrt2 cm`
So, radius of the circle,
`OF=20sqrt2 cm`
Therefore area of the shaded region,
`"Area of the shade region=(Area of quadrant of circle)-(Area of square)"`
So,
Area of the shaded region =`(pi(OF)^2)/4-(OE)^2`
`(22/7)((20sqrt2^2)/4)-(20)^2`
=`628-400`
`=228 cm^2`
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