2005 AMC 12B 第 7 题

Find the intercepts on the two axes

The graph is a rhombus with diagonals along the axes

Setting $y = 0$ gives $|3x| = 12,$ so $x = \pm 4.$ Setting $x = 0$ gives $|4y| = 12,$ so $y = \pm 3.$

The graph is a rhombus with vertices $(\pm 4, 0)$ and $(0, \pm 3),$ so its diagonals have lengths $8$ and $6.$

Its area is $\dfrac12 \cdot 8 \cdot 6 = 24.$

Thus, the correct answer is D.