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Question
In the given figure, a circle is inscribed in an equilateral triangle ABC of side 12 cm. Find the radius of inscribed circle and the area of the shaded region.
[Use `sqrt(3)= 1.73, pi = 3.14]`
Solution
We can find the radius of the incircle by using the formula
`"r" = 2xx"Area of triangle"/"Perimeter of triangle" = (2xxsqrt(3)/4xx(12)^2)/(3xx12) = 2sqrt(3) "cm"`
Now, area of shaded region = Area of triangle - Area of circle
`= sqrt(3)/4xx(12)^2-3.14xx(2sqrt(3))^2`
=62.28-37.68
= 24.6 cm2
Hence, the area of shaded region is 24.6 cm2
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