A Challenge

[A-Man]

Can any body figure how??
I don't know the answer my self.

[mfc]

Hypotenuse of triangles looks like they are smooth but one of them is not straight. I don't remember which wasn't straight... But i'm in my mobile right now i can't see the picture bigger than it... Maybe you can see which is not smooth...

[Silverthorn]

Try to solve it yourself, if you can't get it worked out, look here

Spoiler (Click to View)

The red and dark green triangles don't have the same slope. Red has 3/8 (=0.375), dark green 2/5 (=0.4). In the upper image, there is a slight bend towards the inner side, the lower image is bulged to the outside.

It looks like the whole triangle covers an area of 13x5/2 = 65/2 = 32.5 squares, although, counting each triangle itself gives 7+8+(2x5)/2+(3x8)/2 = 32 squares (as the bottom image has an additional free square its area would be 33). The difference of that half square is caused by the bending of the hypotenuse; when it's towards the inside, the missing 0.5 squares are being filled up, in case it's going towards the outside, an additional 0.5 squares from the theoretical area pop up, resulting in.... that

Does this even make sense?

Edit: bummer, ninja'd xD

[A-Man]

(Ignore what was here)
Edit: OMG BP,xmfcx! you both are right! these bold lines tricked me! I just never thaught of calculating it mathmaticaly.