How to calculate this area?

>>8444327
x^2+xy-xh-yh
where h - height of smaller trapezoid

>>8444330
fuck, I messed up
(x^2+xy)/2-(xh+yh)
let it be so, then

File: 1475688310129.jpg (44KB, 620x400px) Image search: [Google]

44KB, 620x400px

>>8444332
I wasn't quite sure whether I'm allowed to introduce h as height, without calculating it from the given variables. But I guess there's no other way.(?) Just wanted to dubble check.

File: 1409362727516.jpg (275KB, 1300x1721px) Image search: [Google]

275KB, 1300x1721px

The whole thing - white bits - green bits = the blue bits

>>8444342
>at_last_I_truly_see.png

>>8444342
I understood that, but the green bits was what made my head hurt.

>>8444327

Er, what's the trick to calculate green area?

>>8444337
h is variable. There is nothing that determines h in the shape. It appears that h=x/4 but it could be anything between 0 and x/2 if the shape is not drawn to scale, which you should always assume.

Is that Hofstadter's butterfly?

>>8444353
Exactly what I was thinking, but there has to be a solution.

File: 1470630559114.jpg (53KB, 640x658px) Image search: [Google]

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Does anyone have an idea where to start proving it as calculatable?

>>8444367
either solution if variable or h=x/4

>>8444412
leave the proof as an exercise for reader ;)

>>8444337
H = (x-y)/2