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### Missing Piece puzzle

Missing Piece Puzzle - 26 September

Below the four parts have been reorganized. The four partitions are exactly the same in both arrangements. Why is there a hole?

1. No idea :'(
whats the ans ??

1. If you calculate the tangents for the smallest angles of both triangles, you'll have for the green one 2/5 = 0,4 and for the red one 3/8 = 0,375. Different tangents for correspondent angles means different angles, that means the triangles are not similar, which, in this case, wouldn't allow the figure to "close" when you rearrange it, UNLESS you slightly distort the lines, which is the case (you can actually see it if you look really close). The missing block is a compensation for the space created by the distortion. :)

2. Every thing looks correct. But if you look closely, you can see that there is no actual hole. The hole that we see here is just compensation of the space which is been covered by the hypotenuses (see the blocks near to the hypotenuses, there are occupying more space in later case).

3. tuffest brain teasers

4. This is not a perfect triangle with all straight lines. See, the red part is 8 unit (base) and three unit (height). The green part is 5 unit (base) and 2 unit (height). If the base of red part is extended by 5 units, it's height will be extended by less than 2 units. This proves that this is not a perfect triangle. The magic white space is a result of this inperfection.

5. because of the arrangement the space has been formed .before arranging them in anew way , the yellow tiles were exactly fitted on green ones forming a rectangle of 5 X 3on which the other triangles were fitted perfectly.

6. this is not a perfect triangle, as nksaini said, because look at the green one, if you flip it, and put it with the yellow one, there will be a space left at the right bottom..

7. The slopes of the trianle hypotenuses are different. In the upper diagram, the green triangle slope is 2/5, the red triangle is 3/8. The resultant triangle in the lower figure has a slope of 5/13. The white block is the area in the upper triagle between the triangles depicted and a straight line drawn between the upper point on the right and the lower point on the left.

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1. Arrangement of the pieces is the cause of hole .

9. the red tringle is 9*3 w*h in the upper arrangement.
the same red tringle is 8*3 w*h in the lower one.
thers your missing square 9-8=1.

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2. you can check the area difference by calculating the areas of the shapes themslvs & adding them together for each group. A1 - A2 = 1
[w*h]/2 for the triangles. number of squares in each none uniform rechtangle. XD

3. you can get as many sets of corresponding triangles that are made by the rectangle whose edge slides across the slope of the larger triangle as the mathimatically corresponding intersections with unitary points. I think a trickier triangle can be made using a (w=h) ratio.

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11. the second pic is not a triangle but a trapezium