seekmba wrote:

How can we find the area of equilateral triangle if we know just the height of equilateral triangle (say 3/2)?

Let say the side of an equilateral triangle is \(b\).

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Now, the height of equilateral triangle is also the median, thus it divides the base into half. Half of the base, \(\frac{b}{2}\) and height, \(h\), would be the legs of right triangle and the hypotenuse would be the side of this triangle so \((\frac{b}{2})^2+h^2=b^2\) --> \(b^2=h^2*\frac{4}{3}\) --> \(b=h\frac{2}{\sqrt{3}}\) --> \(area=\frac{1}{2}*height* base=\frac{1}{2}*h*h\frac{2}{\sqrt{3}}=\frac{h^2}{\sqrt{3}}\)

Or: as the hight divides the equilateral triangle in two 30-60-90 triangles then the sides of these triangles will be in the ratio \(1:\sqrt{3}:2\), so if height (the side opposite 60 degrees) is \(h\) then the side of the equilateral triangle (the side opposite 90 degrees) will be \(h*\frac{2}{\sqrt{3}}\) and the \(area=\frac{1}{2}*h*h\frac{2}{\sqrt{3}}=\frac{h^2}{\sqrt{3}}\).

For more on triangles check Triangles chapter of Math Book.

Hope it helps.

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