AMC 12 2019a Problem 5

Two lines with slopes $\dfrac{1}{2}$ and $2$ intersect at $(2,2)$. What is the area of the triangle enclosed by these two lines and the line $x+y=10$?

$\textbf{(A) } 4 \textbf{(B) } 4\sqrt{2} \textbf{(C) } 6 \textbf{(D) } 8 \textbf{(E) } 6\sqrt{2}$