A triangle has vertices at (0,0), (6,0), and (0,8). What is the area of the triangle?

The vertices $(0,0)$, $(6,0)$, and $(0,8)$ form a right triangle with the right angle at the origin. The leg along the $x$-axis has length 6 and the leg along the $y$-axis has length 8, so they act as base and height: $\text{Area} = \frac{1}{2}(6)(8) = 24$. A common wrong answer is 48, which is the area of the full rectangle with those legs, forgetting the factor $\frac{1}{2}$. Another is 14, from adding the legs instead of multiplying, and a third is 10, the hypotenuse. Area needs the base and height at right angles, which the axes provide here.