2013 AMC 10A Problem 16

The reflected triangle has vertices $(7,1)$, $(8,-3)$, and $(10,5)$. The line through $(6,5)$ and $(9,1)$ is $y=-\frac43x+13$, so it meets $x=8$ at $y=\frac73$. By symmetry, the union is two congruent triangles with vertical base from $(8,-3)$ to $(8,\frac73)$. That base has length $\frac73+3=\frac{16}{3}$, and each triangle has horizontal height $2$. Hence the union area is $2\left(\frac12\cdot\frac{16}{3}\cdot2\right)=\frac{32}{3}$. Thus, E is the correct answer.