解$: (2)$因为$(a + b)^2=a^2+b^2+2ab,$
$ 92^2+16×92 + 64=92^2+2×8×92 + 8^2=(92 + 8)^2=100^2=10000$
$ (3)$根据题意,得$\frac {1}{2}ab = 3,$即$ab = 6。$
$ $因为$a,$$b$均为正整数,
所以$a = 1,$$b = 6$或$a = 2,$$b = 3。$
$ $所以$a^2+b^2=1 + 36=37$或$a^2+b^2=4 + 9=13。$
$ $所以题图$②$中$2$个小正方形面积的和为$37$或$13$