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hole in the triangle mystery

Hello guys, now i want to share to you some interesting problem namely missing square puzzle . Hmmm

Okay we try to solve it together, hehehe,.. I think to solve it, first we must know that there is a geometrical illusion in both of these pics.  could you see the one that i mean??? Try to focus in a meeting point between the red and blue (cyan) triangle

Hmm,.. In fact a meeting point between the red and cyan triangle. They don’t form a straight line at the point of its exterior angle is not exactly 180 degrees ???

Here is the calculation of the value of the angle between the outside of the triangle red and cyan triangle in the first picture:
360-(90+ atan (2/5) + atan (8/3)) = 178. 755 not 180 degree??

Here is the calculation of the value of the angle between the outside of the red triangle and a cyan triangle in the second picture:
360-(90+ atan (5/2) + atan (3/8) = 181. 245 and neither is it??

Well if we make an imaginary line that connects the upper right corner point and the lower left corner, we can create a new triangle with three sides that (imaginary line, the red triangle hypotenuse and cyan triangle hypotenuse). Okay we call this new triangle with the name “shucks triangle”

Back again to the second picture. If both the flat wake overlaid, it will generate a new triangle. Triangles are included in the intersection of second triangles and first triangle. can you imagine that??? I hope you can xixixixi

If we give more attention for the new shape that we get due to the process above, we will know that the area of ​​new shape that we have created is doubling of “shucks triangle ”

To know the area of  “shucks triangle” we can use simple sine and Pythagoras rules approach. Hey you still with mee right??? we continue it …….

If you can’t imagine the triangle that i mean, okay i will show you about it, i get this pic while i brows in wikipedia 🙂

See the shape that i describe before.. (source: http://en.wikipedia.org/wiki/Missing_square_puzzle)

The area of ​ “shucks triangle” calculated using the approach of sine rule —->  L = 1 / 2bc sin <alpha

So the area twice a triangle shucks it is as follows

2 × (0.5) sin (360-(90+ atan (2/5) + atan (8/3))) × (2 ^ 2 + 5 ^ 2) ^ (0.5) × (8 ^ 2 + 3 ^ 2 ) ^ (0.5) = 1

Answered already why emerging area of ​​one square hole in the triangular part two