3. (8 points) The figure shown is the emblem of the Yingchun Primary School Mathematics Interest Group. Among them, $A B C D E F$ is a regular hexagon with an area of 360. What is the area of quadrilateral $A G D H$?
160
【Solution】Solution: According to the analysis, (1) the area of $\triangle A B C$ is equal to $\frac{1}{6}$ of the area of the hexagon. Connecting $A D$, the quadrilateral $A B C D$ is $\frac{1}{2}$ of the area of the regular hexagon, so the area of $\triangle A C D$ is $\frac{1}{3}$ of the area of the regular hexagon.
(2) $S_{\triangle A B C}: S_{\triangle A C D}=1: 2$. According to the kite model, $B G: G D=1: 2$;
(3) $S_{\triangle B G C}: S_{\triangle C G D}=B G: G D=1: 2$, so $S_{\triangle C G D}=\frac{1}{6} \times \frac{2}{3} \times 360=40$; thus, the area of $A G D H$ = the total area of the hexagon - $\left(S_{\triangle A B C}+S_{\triangle C G D}\right) \times 2=360-\left(\frac{1}{6} \times 360+40\right) \times 2=160$. Therefore, the answer is: 160