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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