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[Frits]

hol vs bol

Als je van een afstandje kijkt zie je het idd... hol vs bol

If AB were a straight line, then ANM would have to be similar to MOB. That is, the slope of AM would have to be the same as the slope of MB. But the slope of AM is

formula

and the slope of MB is

formula

If ABC were a triangle, its area would be

formula

Similarly if DEF were a triangle, its area would be

formula

But if we add up the areas of the pieces of ABC we get a different result

red triangle


=


12

green triangle


=


5

L-shaped orange object


=


7

L-shaped green object


=


8

for a total area of 32 square units.

If we add up the areas of the pieces of DEF we get 33 square units, the same as for ABC plus one more for the white square.

So, ABC is slightly less than a triangle and DEF is slightly more than a triangle. Look closely.