Consider a as the side of an equilateral triangle
We know that
Height of an equilateral triangle = √3/2 a
It is given that height = 9cm
So we get
√3/2 a = 9
On further calculation
a = (9 × 2)/ √3
Multiplying both numerator and denominator by √3
We get
a = (9 × 2 × √3) / (√3 × √3)
So we get
Base = a = 6√3cm
We know that the area of an equilateral triangle = ½ × b × h
By substituting the values
Area of the equilateral triangle = ½ × 6√3 × 9
On further calculation
Area of the equilateral triangle = 27√3 cm2
By substituting the value of √3
Area of the equilateral triangle = 27 × 1.732 = 46.764
By correcting to 2 places of decimal
Area of the equilateral triangle = 46.76 cm2
Therefore, the area of an equilateral triangle = 46.76 cm2.
