2008 AMC 12A 第 14 题

The region is a rhombus centered where $3x - 18 = 0$ and $2y + 7 = 0$

Its horizontal diagonal spans $x \in [5, 7]$ and its vertical diagonal spans $y \in [-5, -2]$

The region is a rhombus centered at $\left(6, -\tfrac{7}{2}\right).$ Setting $2y + 7 = 0$ gives $|3x - 18| \le 3,$ so $x \in [5, 7],$ a horizontal diagonal of length $2.$

Setting $3x - 18 = 0$ gives $|2y + 7| \le 3,$ so $y \in [-5, -2],$ a vertical diagonal of length $3.$

The area of the rhombus is half the product of its diagonals, $$\dfrac{1}{2} \cdot 2 \cdot 3 = 3.$$

Thus, A is the correct answer.