There are very few things I will loose sleep over (space: it never ends, yet it must!) and it pains me to say that the following is one of them. There's a high chance that I'm just being a reject and overlooking something obvious, but I can't rest until I know the answer!
I can't understand why they should have the same area, but apparently don't. If you add up the areas of each individual piece it equates to 32 units. If you take the area of the top triangle it equates to 32.5 units. :?
ive seen this before. trust me, if u dont want your brain to fry, dont think about it too hard. i was so crazy about this i printed it out and experimented with it. results: orange for a head. dont know why, so dont ask why :lol:
What I should have been clearer on was my question. After re-reading my post, and looking at what I now see to be a misleading picture, I feel I should explain.
The hole in the bottom triangle: they are arranged differently and so the bottom triangle isn't really a triangle, I can accept this.
Now lets forget the bottom triangle. If we take each piece of the top triangle we have the following.
Red triangle: Area = 0.5(8*3) = 12 units
Green triangle: Area = 0.5(5*2) = 5 units
Green shape: Area = 8 units (simply from counting the boxes)
Yellow shape: Area = 7 units (from counting the boxes)
Cummulative area of these shapes = 12+5+8+7 = 32 units.
Now lets take the area of the full triangle, with all pieces arranged together: Area = 0.5(5*13) = 32.5 units.
What I would like to know is there this extra 0.5 units of area comes from.
The way I see it is that the hole just comes from the fact that the 2 figures are not in fact triangles and have different areas. It's more simple than you think.
All is well. The top "triangle" is not a triangle at all, but rather, a four-sided shape.
The hypotenuse (slope) is not a straight line.
If you take the angle between the hypotenuse and bottom of the green triangle: invtan(2/5) = 21.801 degrees.
And of the red triangle: invtan(3/8) = 20.556 degrees.
This would explain the difference in area as we cannot use the equation, Area = 0.5*length*base.
Daz: I am no longer offering you money for your solution. :lol:
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