Given: Area of each smaller equilateral triangle =9√3cm2 Concept Used: Area of equilateral triangle =√3a2∕4 Height of equilateral triangle =√3a∕2 Where, a= side of the equilateral triangle Calculation:
Let the side length of each smaller triangle be a cm Since the area of each smaller equilateral triangle =9√3cm2 So, √3a2∕4=9√3 ⇒a=6cm So, the side of bigger equilateral triangle ABC=6×3=18cm So, Height AD of the bigger equilateral triangle =(√3×18)∕2=9√3cm ∴ The required height of the bigger equilateral triangle is 9√3cm .