What is the area of an equilateral triangle with height of 9√3cm?

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Answer 1 · 2018-03-07T03:58:24

#color(brown)(A = (sqrt3 / 4) * 18^2 = 81 sqrt3 = 140.3# #cm^2#

Equilateral triangle
enter image source here

From the above figure,

#h = (sqrt3/2) s = 9 sqrt3 cm# where s is the measure of a side.

#s = (9 cancelsqrt3) / (cancelsqrt3 / 2) = 18 cm#

enter image source here

Area of equilateral triangle #A = (sqrt3 / 4) * s^2#

#color(brown)(A = (sqrt3 / 4) * 18^2 = 81 sqrt3 = 140.3# #cm^2#