a — height of a white tile
b — width of a white tile
a x b — S₁, area of a white tile (this is what we are trying to "find")
(a - b)² — S₀, area of a black square
(a + b)² — S, area of a whole block (4 white tiles, 1 black tile)
Now, looking at the image it is obvious, that (S - S₀) = 4S₁.
a — height of a white tile
b — width of a white tile
a x b — S₁, area of a white tile (this is what we are trying to "find")
(a - b)² — S₀, area of a black square
(a + b)² — S, area of a whole block (4 white tiles, 1 black tile)
Now, looking at the image it is obvious, that (S - S₀) = 4S₁.