2. The three sides of a triangle $a, b, c$ are all integers, and satisfy $a b c + b c + c a + a b + a + b + c = 7$. Then the area of the triangle is equal to ().
(A) $\frac{\sqrt{3}}{2}$
(B) $\frac{\sqrt{2}}{4}$
(C) $\frac{\sqrt{3}}{4}$
(D) $\frac{\sqrt{2}}{2}$
2. (C).

From $8=a b c+b c+c a+a b+a+b+c+1$ $=(a+1)(b+1)(c+1)$,

and $8=8 \times 1 \times 1=4 \times 2 \times 1=2 \times 2 \times 2$,
we can deduce that $a+1=b+1=c+1=2 \Rightarrow a=b=c=1$.
Therefore, the area of an equilateral triangle with side length 1 is $\frac{\sqrt{3}}{4}$.