Volume: $V=abc\ge 1001$ half Area $A_2=\frac{A}{2}=ab+bc+ca$ WLOG: $a \le b \le c$ $a=b=10$ $c=11$, $V=1100$, $A_2=320$ Then $a \le 10$ If $a\le 3$ then $334 \le bc \le A_2$ then $a \in \{4,5,6,7,8,9,10\}$ Notice that $\frac{1001}{a} \le bc$ and $A_2=a(b+c)+bc$ Checking some cases to find $(a,b,c)=(7,12,12)$

The right answer is $(8,9,14)$