The area of rectangle ABCD is 1728 $\text{cm}^2$. The length of FE is $\frac{5}{6}$ of the length of AD. What is the area of the triangle ABE? Ans: ___ $\text{cm}^2$

1. Express the area of the rectangle in terms of its sides

Area of rectangle $ABCD = AB \times AD = 1728$

2. Express the area of triangle ABE in terms of AB and FE

Area of triangle $ABE = \frac{1}{2} \times AB \times FE$

3. Substitute FE in terms of AD and calculate the area

Since $FE = \frac{5}{6} AD$,
Area of triangle $ABE = \frac{1}{2} \times AB \times (\frac{5}{6} AD)$
$= \frac{1}{2} \times \frac{5}{6} \times (AB \times AD)$
$= \frac{5}{12} \times 1728$
$= 720$