the height of an equilateral triangle measures 9cm.find its area.correct to two places of decimals(take sq. root3=1.73)

Given, height of an equilateral triangle = 9 cm and √3 = 1.73

Now, consider an equilateral triangle ABC having AD altitude from A to the base BC.

So, AD = 9 cm

Let AB = BC = AC = x cm

We know that, in an equilateral triangle altitude from the vertex will always bisect the base.

Therefore, BC = BD + DC

⇒ 2 BD = x

⇒ BD =

In Δ ABD by Pythagoras theorem, we have

AB² = AD² + BD²

⇒ x² = 9² + ()²

⇒ x² - = 81

⇒

⇒

⇒

So, the length of side of equilateral triangle = cm

We know that, area of an equilateral triangle = =

=