How can this be true?

[KoChun]

Can somebody solve this problem for me, please? Keep giving me sleepless nights for the past few days.



http://server3.uploadit.org/files/KoChun-triangle.jpg

[shiruikage]

http://i6.photobucket.com/albums/y247/shiruikage/KoChun-triangle.jpg
i believe i knew the answer. notice how the three circled area fills up extra areas from the top image? it all adds up to exactly half of unit. the other half of unit comes from error of area calculation probably. as the Area for each object is less then the total object as a whole by 0.5 units.

the total triangle is 32.5 unit squared. individual objects are 5 and 12 for the triangles, and 7 and 8 for the orange and green objects. total is 32. but since the total left out area is 1 unit, that leaves 0.5 unit unaccounted for, that that is y i beliv its in the three circled areas. the triangle is ...bigger this way...???

[daBoss]

the answer to this problem is simple...

the gradient of the slopes in the green and red triangles are not the same although almost equal:
1. green = 2/5
2. red = 3/8

so our eyes deceive us by tricking us to think that the combined slope is a straight line - it's not:
1. in the first diagram, the combined slope is actually a very unnoticeable valley
2. in the second diagram, the combined slope is actually a very unnoticeable hump

the difference in area between the valley and the hump is exactly 1 box - hence the extra empty box.

:)

[Sarah]

its all maths and calculation laa...

[shiruikage]

well, at least i got some part right! :laugh: :o