by **gad123**

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That's quite clever, that is. The key thing is that the overall shape you are perceiving as a triangle is in fact a quadrilateral.

The gradient of the green triangle is slightly different to the gradient of the red triangle. The red triangle's gradient is 3/8 = 0.375 wherease the gradient of the green triangle is 2/5 = 0.4. The top figure is therefore slightly concave and the lower one is slightly convex, giving them very slightly different areas.

If you work out the area of each shape in the puzzle you'll find:

Red Triange = 12 (8 x 3 / 2)

Green Triangle = 5 (5 x 2 / 2)

Yellow shape = 7

Green shape = 8

Total = 32

yet the total expected area of the overall figure is 13 x 5 / 2 = 32.5.

The best way to view the discrepancy is by overlaying the bottom figure onto the top figure. Then you will clearly see that the slope of the top of what you perceive as being the triangles doesn't actually line up. The area of this overlap can be shown to be exactly 1 unit of area which is the gap you see in the bottom figure..

14th Oct 2005, 01:11