Question

Using Pythagoras theorem, prove that the area of an equilateral triangle of side ‘a’ is √3/4*a^2

Answer 1

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Answer 2

Let the side of triangle be a.

 

Now, Semiperimeter of triangle = (a + a + a)/2 = 3a/2

 

Area of triangle by Heron's formula = 

Now, s - a = (3a/2) - a = a/2

 

And, a = b = c = a (Equilateral triangle)

 

Thus, Area = √3/4a×a^2

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