In an equilateral triangle the radius of inscribed circle is equal to [tex]r= \frac{a \sqrt{3} }{6} [/tex], so [tex]5 \sqrt{3} = \frac{a \sqrt{3} }{6} [/tex] and [tex]a=30[/tex]. The area of this equilateral triangle is [tex]A= \frac{a^2 \sqrt{3} }{4} =\frac{30^2\cdot \sqrt{3} }{4}=225 \sqrt{3} [/tex] square units.
