Find the area of an equilateral triangle if its height is 6cm.

1. The tops of the triangle A, B, C. BE = 6 centimeters – height.

2. All angles of this triangle are 60 °.

3. We calculate the length of the segment AE through the tangent ∠A of the right-angled triangle ABE:

Tangent ∠A = BE / AE.

Tangent ∠A = tangent 60 ° = √3.

BE / AE = √3.

AE = 6 / √3 = 2√3 centimeters.

4. Calculate the area (S) of the triangle ABC:

S = AC x BE / 2.

AC = AE + CE = 2√3 + 2√3 = 4√3 centimeters.

S = 4√3 x 6/2 = 12√3 centimeters².

Answer: the area of the triangle ABC is 12√3 centimeters².