A circle is inscribed in an equilateral triangle of side `adot` The area of any square inscribed in this circle is ______.

Answer

`(a^(2))/(6)`sq unit

Explanation

In an equilateral triangle, the radius of incircle
`=(1)/(3)xx` median of the triangle
`=(1)/(3)sqrt(a^(2)-(a^(2))/(4))=(1)/(3)sqrt((4a^(2)-a^(2))/(4))=(a)/(2sqrt3)`
therefore ,area of the square inscribed in this circle
`=2("radius of circle")^(2) = (2a^(2))/(4*3)= (a^(2))/(6)` sq unit