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  • Prove that the area of an equilateral triangle described on one side of the square is equal to half the area of the equilateral triangle described on one of its diagonal.      

Prove that the area of an equilateral triangle described on one side of the square is equal to half the area of the equilateral triangle described on one of its diagonal.  

 

 

 
 
 
 
 

Answers (1)

Here ABCD is a square and let the side of the square be 'a' unit 

AC^2 = a^2 +a^2 = 2 a^2 \\\\ AC = \sqrt 2 a \: \: units

Area of equilateral triangles \Delta BCF = \frac{\sqrt3}{4} a ^2 \: \: sq . units \\\\

Area of equilateral triangles 

\Delta ACE = \frac{\sqrt3}{4} (\sqrt2 a)^2 \: \: sq . units \\\\ = \frac{\sqrt 3 }{2} a^2 \: \: sq. units

Area \Delta BCF = \frac{1}{2} Ar \: \: \Delta ACE

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