Question

If the area of a circle, inscribed in an equilateral triangle is 4π cm², then what is the area of the triangle?

(a) 12√3 cm² 

(b) 9√3 cm² 

(c) 8√3 cm² 

(d) 18 cm²

Answer 1

(a) 12√3 cm²

Since area of circle = 4π ⇒ πr² = 4π ⇒ r = 2 cm

In ΔOAD,

tan 30° = \(\frac{OD}{AD}\) ⇒ \(\frac{1}{\sqrt3}\) = \(\frac{2}{AD}\)

⇒ AD = 2√3 cm 

∴ AB = 2AD = 4√3 cm

∴ Area of equilateral ΔABC = \(\frac{\sqrt3}{4}\) (AB)²

= \(\frac{\sqrt3}{4}\) (4√3)² = 12√3 cm².