How do you find the area of this trapezoid

Question

How do you find the area of the trapezoid $KCDL$?

Answer 1

Let $P$ be the midpoint of $KL$, and $Q$ be the midpoint of $CD$.

Then by similar triangles:

$$\frac{CQ}{AQ} = \frac{KP}{AP}$$ $$\frac{6}{48} = \frac{KP}{36}$$ $$KP = 4.5, KL = 9$$

Now use the formula for the area of a trapezoid: $$\frac{a+b}{2} \cdot h$$