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In an equilateral triangle with side a, prove that area = √3/4 a2.

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Let ABC be the equilateral triangle with each side equal to a. 

Let AD be the altitude from A, meeting BC at D. 

Therefore, D is the midpoint of BC. 

Let AD be h.

 Applying Pythagoras theorem in right-angled ABD, we have: 

AB2 = AD2 + BD2

Therefore, 

area of triangle  ABC = 1/2 × base × height = 1/2 × a × √3/2 a 

This completes the proof.

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