Question

in a triangle a circle of radius 1 cm radius is inscribed find the area of the equilateral triangle​

Answer 1

Area of equilateral triangle =

\frac{\sqrt{3}}{4} a^2

Semi perimeter of equilateral triangle = (a + a + a) / 2

Radius of inscribed circle r = Area of equilateral triangle / Semi perimeter of equilateral triangle. =

\frac{\sqrt{3}}{4} a^2 / {\frac{3a}{2}}

=

\frac{a}{2{\sqrt3}}

Area of circle = PI*(r*r) =

\frac{\pi a^{2}}{12}