In the bottom triangle you can easily (well, it’s not that hard) work out where that hole came from. We all agree that the bottom triangle bulges out a bit along its fake hypothenuse. There is an extra sliver of a triangle that consists of the hypothenuses of the three right triangles in the picture. Those three right triangles have sides: 2, 5, sqrt(29) [small green triangle]; 3, 8, sqrt(73) [big red triangle]; and 5, 13, sqrt(194) [big one that includes the other two]. The sliver triangle has sides sqrt(29), sqrt(73), and sqrt(194). Now use Heron’s formula to find its area. You will find that area to be exactly .5. By the same approach the top triangle bulges in by exactly that same amount of .5. Add them together and you have the missing area of 1 in the bottom figure.
I looked at it for a while and couldn’t get it – I was being obtuse.
Riiiiiiiight :rolleyes:.
That’s acute joke!