Using
[OQL]=OL . KL/2=bc/2
[OPQ]+[LKQ]=PQ . KL/2+QK.KL/2=(PQ+QK).KL/2=PK.KL=bc/2
=>[OQL]=[OPQ]+[LKQ]=bc/2
[OPKL]= [OQL]+[OPQ]+[LKQ]=2bc/2=bc
In the same way [LMHI]= [IJEF]= [FGNO]= [OPKL]= bc
[QRST]= [OLIF] + [OQL] + [LRI] + [ISF] + [FTO]
[QRST]= c^2+2bc=c(c+2b)
Therefore [QRST]= ac (Situation A)
But, this is not true if b is too big, then the square cannot touch the external square…
[STUV]=[PQKG]+4[PSQ]
∠PSQ=π/2=> [PSQ]=c^2/4
[STUV]=[PQKG]+4[PSQ]=c^2+c^2
Therefore [STUV] = 2c^2 (situation B)
The limit between the is when Situation A=Situation B
The limit is when Situation A=Situation B
When c^2+2bc=2c^2
When c=2b
If c>2b then [QRST]= ac
If c<2b then [STUV] = 2c^2