4. In the diagram, $\angle A F C=90^{\circ}, D$ is on $A C$, $\angle E D C=90^{\circ}, C F=21, A F=20$, and $E D=6$. Determine the total area of quadrilateral $A F C E$.
4. The area of quadrilateral $A F C E$ equals the sum of the areas of $\triangle A F C$ and $\triangle A C E$.
Since $\triangle A F C$ is right-angled at $F$, then its area equals $\frac{1}{2}(A F)(C F)=\frac{1}{2}(20)(21)=210$.
Since $\triangle A F C$ is right-angled at $F$, then we can use the Pythagorean Theorem to obtain
$$
A C=\sqrt{A F^{2}+C F^{2}}=\sqrt{20^{2}+21^{2}}=\sqrt{841}=29
$$
since $A C>0$.
Since $E D$ is perpendicular to $A C$, then $\triangle A C E$ can be viewed as having base $A C$ and height $E D$.
Therefore, the area of $\triangle A C E$ is $\frac{1}{2}(A C)(D E)$ or $\frac{1}{2}(29)(6)$ or 87 .
Thus, the area of quadrilateral $A F C E$ is $210+87=297$.