2016 AMC 10A Problem 11

We can split the region into $4$ triangles with bases of $1.$ All four triangles have base $1.$ Two have height $8\div2=4,$ and the other two have height $5\div2=\dfrac52.$ The sum of the areas of the triangles is $$\begin{aligned} &2 \cdot \dfrac{1}{2} \left(1 \cdot \dfrac{5}{2}\right) \\ &\quad {}+ 2 \cdot \dfrac{1}{2} \left(1 \cdot 4\right) = 6\dfrac{1}{2} \end{aligned}$$ Thus, the correct answer is D .