Use the coordinate geometry formula for the area of a triangle with vertices $P(8, 12)$, $Q(10, 8)$, and $R(8, 2)$.

Since $P$ and $R$ share the same $x$-coordinate ($x = 8$), $\overline{PR}$ is a vertical segment:

$\text{Base} = PR = |12 - 2| = 10$

The height is the horizontal distance from $Q$ to the line $x = 8$:

$\text{Height} = |10 - 8| = 2$

$\text{Area} = \frac{1}{2} \times 10 \times 2 = 10$