Luriga Triangle..

[blike]

Suppose a triangle is made up of various different shapes. No matter how you rearrange those shapes, the area should still be the same, correct?

 

 

Either I'm missing something obvious, or its been too long since I've taken geometry..

[aman]

Thank you Blike. This is a fun one for someone who hasn't calculated sines and cosines for ages.

Just aman

[fafalone]

Well just looking at it I see what they did.

 

The two triangular parts were switched, creating room for the orange part to move off the top of the green on onto the other part. This created an extension of 3 units, compared with the 5 units, so you have 2 extra units left, the bottom of it is 2 units, so you wind up with one extra unit.

[blike]

Right, but what about the total area? No parts changed, so the area should be the same, yet its not?

[fafalone]

The "total" area does not change, just the area of the triangle.

[aman]

The angles of the two triangle parts are not equal so switching them on the second figure does not give you a true hypotenuse. It bulges to an area of 1 square. I'll let you do the math

Just aman

[Radical Edward]

the angles of the two big triangles are different, so the 'triangle' that you percieve there is actually a 4 sided shape, and not three. the trick relies on the fact that humans have crap eyesight.

[blike]

Yea, I realized that when I checked the sin for each.