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Prove that the area of an equilateral triangle is equal to √3÷4×a² where a is the side of the triangle.

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by Guga789

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by Guga789

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The Brainliest Answer!

height = square root of(side² - (side/2)² by pythagoras theorem

= √s²-s²÷4

= √(4s²-s²)/4

=√3s²/4

= √3 x s/2

area = 1/2 x b x h

= 1/2 x s x √3 x s/²

= √3/4 s²

according to the pythagorean theorem :

Each right angle triangle area is . And the area of the equilateral triangle is double of that.

( a can be x) ( means √)