2018 AMC 10A Problem 9

We know that the side length of the smaller triangles is $\sqrt{\frac{1}{40}}$ times the length of the larger triangle from similar triangles. Then the side length of $\triangle ADE$ is $4\sqrt{\frac{1}{40}}$ times the length of the side length of the larger triangle. This makes the ratio of the areas $$\left(4\sqrt{\dfrac{1}{40}}\right)^2 = 16 \cdot \dfrac{1}{40} = \dfrac{2}{5}.$$ Therefore, the area of $\triangle ADE$ is $\frac{2}{5} \cdot 40 = 16.$ The area of the trapezoid is then $40 - 16 = 24.$ Thus, E is the correct answer.