[填空题]
The quadrilateral ABCD represents a recreatiov:6vhi k+o+ncnal park, where AB =250 m, BCghi7-8h nxf k9 =110 m and CD =130 m. Anglhx gh k7n-9f8ie $\mathrm{A}\hat{\mathrm{B}}\mathrm{C}$ is $80^{\circ}$ and angle $\mathrm{C}\hat{\mathrm{D}}\mathrm{A}$ is $115^{\circ}$. This information is shown in the following diagram.
A straight path through the park joins the points A and C.
1.Find the length of the path AC. m
2.Show that the angle $\mathrm{D}\hat{\mathrm{A}}\mathrm{C}$ is $27.5^{\circ}$, correct to three significant figures. $^{\circ}$
3.Find the total area of the recreational park. $m^2$
A new path, DE, is to be built such that E is the point on AC closest to D.
4.Find the length of the path DE. m
The section of the park represented by triangle CDE will be used for a school cross country carnival. A track will be marked along the sides of this section.
