Gogeometry Problem 356

 dans Euclide Geometry Problem par Harvey Littleman

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From Gogeometry

Using :

• Area of a triangle

• Define h1,h2,h3 and h4 the heights respectively of S1, S2, S3 and S4
• Define a the side of the square ABCD
• S1=a.h1/2
• S2=a.h2/2
• S3=a.h3/2
• S4=a.h4/2
• And h1+h3=h2+h4=a
• S1+S3=a(h1+h3)/2=a^2/2
• S2+S4=a(h2+h4)/2=a^2/2
• S=[ABCD]=a^2
• Therefore S1+S3= S2+S4=S/2

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