In the diagram, points $P(2,6), Q(2,2)$ and $R(8,5)$ form a triangle. The area of $\triangle P Q R$ is
(A) 24
(B) 14
(C) 21
(D) 12
(E) 16

![](https://cdn.mathpix.com/cropped/2024_04_20_ac36362783317e0251fdg-008.jpg?height=518&width=512&top_left_y=1728&top_left_x=1224)
The given triangle can be considered to have base $P Q$ (which is vertical along the line $x=2$ ) and perpendicular height which runs from $R$ horizontally to $P Q$.

The line segment joining $P(2,6)$ to $Q(2,2)$ has length 4 .

Point $R(8,5)$ is 6 units to the right of the line with equation $x=2$.

Thus, $\triangle P Q R$ has area $\frac{1}{2} \cdot 4 \cdot 6=12$.

ANSwER: (D)