Use the parametric equations of an ellipse \[ \begin{array}{l} x=12 \cos \theta \\ y=17 \sin \theta \\ 0 \leq \theta \leq 2 \pi \end{array} \] to find the area that it encloses.

Step 1 ：Given the parametric equations of an ellipse: \(x=12 \cos \theta\), \(y=17 \sin \theta\), where \(0 \leq \theta \leq 2 \pi\).

Step 2 ：The area of an ellipse is given by the formula \(\pi ab\), where \(a\) and \(b\) are the semi-major and semi-minor axes respectively.

Step 3 ：In this case, \(a=12\) and \(b=17\).

Step 4 ：Substitute these values into the formula to find the area: \(\pi \times 12 \times 17\).

Step 5 ：Calculate the area to get approximately 640.8849013323178.

Step 6 ：Final Answer: The area that the ellipse encloses is \(\boxed{640.88}\).