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The altitude of an equilateral triangle bisects the base.

So, if the sides of the triangle were l cm, the altitude forms a right angled triangle with sides h, l/2 and hypotenuse l cm.

Then, by Pythagoras, h2 = 3l2 / 4 so that h = l*sqrt(3)/2

and then area = l*h/2 = l*[l*sqrt(3)/2]/2 =l2*sqrt(3)/4

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Q: Find the area of an equilateral triangle with altitude h cm?
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