Question

If the distance from the vertex to the centroid of an equilateral triangle is 6 cm, then what is the area of the triangle?

(a) 24 cm² 

(b) 27√3 cm² 

(c) 12 cm² 

(d) 12√3 cm²

Answer 1

(b) 27√3 cm² 

Here OA = 6 cm ∴ OD =\(\frac{OA}{2}\) = 3 cm

AD = 6 cm + 3 cm = 9 cm 

Let each side of ΔABC be x cm. 

From right angled ΔADB,

AB² - BD² = AD²