For 6.28: Let $\overline{AD}$ be the larger base of the trapezoid, with diagonal $\overline{AC} = 10$. Extend line segment $\overline{AD}$ to a point $E$, such that $EACB$ is a parallelogram.  Since you want to find the area of the trapezoid, and you know its height, the goal is to find $\overline{AD} + \overline{BC}$.

For 6.29: Use the fact that if the ratio of the sides of similar triangles is $1 : r$, then the ratio of their areas is $1 : r^2$. For example, since $\triangle ADE \sim \triangle AFG$, we have that $$\dfrac{[AFG]}{[ADE]} = \dfrac{AF^2}{AD^2}.$$