Rectangle $A B C D$ has area 2016. Point $Z$ is inside the rectangle and point $H$ is on $A B$ so that $Z H$ is perpendicular to $A B$. If $Z H: C B=4: 7$, what is the area of pentagon $A D C B Z$ ?

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The area of pentagon $A D C B Z$ equals the area of rectangle $A B C D$ minus the area of $\triangle A Z B$.

Since the area of rectangle $A B C D$ is 2016 , then $A B \cdot C B=2016$.

The area of $\triangle A Z B$ equals $\frac{1}{2}(A B)(Z H)$.

Since $Z H: C B=4: 7$, then $Z H=\frac{4}{7} C B$.

Thus, the area of $\triangle A Z B$ is $\frac{1}{2}(A B)\left(\frac{4}{7} C B\right)=\frac{2}{7}(A B)(C B)=\frac{2}{7}(2016)=576$.

Therefore, the area of pentagon $A D C B Z$ is $2016-576=1440$.

ANSWER: 1440