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` and π = 3.14.]

Answer 1

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