One way to proceed is to regard the pattern as four arms, each two
squares wide, with four corner pieces of three squares each. So for
the $n_{th}$ pattern, we have $4 \times 2 \times n + 4 \times 3 =
8n +12$. For $n=10$, we need $8 \times 10 +12$, i.e. $92$
squares.