3. As shown in Figure 1, in $\square A B C D$, $A D=a, C D=b$, draw the heights $h_{a}, h_{b}$ from point $B$ to sides $A D$ and $C D$ respectively. Given $h_{a} \geqslant a, h_{b} \geqslant b$, and the diagonal $A C=20$. Then the area of $\square A B C D$ is $\qquad$
3. 200 .

Given $h_{a} \geqslant a, h_{b} \geqslant b$, in addition, $a \geqslant h_{b}, b \geqslant h_{a}$, then $h_{a} \geqslant a \geqslant h_{b} \geqslant b \geqslant h_{a}$, i.e., $h_{a}=a=h_{b}=b$, which means that quadrilateral ABCD is a square.
Since the diagonal of this square $AC=20$, the area of $\square ABCD$ is 200.