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The Brainliest Answer!
2014-03-08T21:21:51+05:30
Base of equilateral triangle = b

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
3 4 3
2014-03-08T21:25:17+05:30
A line perpendicular to the the opposite base which will form 2 right angle triangles. Each right triangle leg length x/2. 

according to the p
ythagorean theorem : x^2=(x/2)^2+h^2

x^2=(x/2)^2+h^2 
x^2-(x/2)^2=h^2 
x^2- x^2/4=h^2 
4x^2- x^2=4h^2 
3x^2/4=h^2 
(√3/2) x=h 

Each right angle triangle area is  (1/2)*(x/2)*h. And the area of the equilateral triangle is double of that.

A = 2*(1/2)*(x/2)*h 
A = (x/2)*h 
A = (x/2)*(√3/2)x 
A = (√3/4) x^2  ( a can be x) (  √ means √)
2 4 2