x1 = 0,  y1 = 0,  x2 = 7,  y2 = 3,  x3 = 11,  y3 = 6
Compute the area of the triangle using Cartesian coordinates.
Let's use the Shoelace formula to compute the area of the triangle with the given Cartesian coordinates. The Shoelace formula is used to find the area of a simple polygon whose vertices are described by their Cartesian coordinates. 

Given the coordinates (x1, y1), (x2, y2), and (x3, y3), the area of the triangle can be calculated by:

Area = 1/2 [| x1(y2 − y3) + x2(y3 − y1) + x3(y1 − y2) |]

Substituting the values in the above formula, we get:

Area = 1/2 [| 0(3 − 6) + 7(6 − 0) + 11(0 − 3) |]

Area = 1/2[| 42 - 33 |] = 9/2 sq units

So, the area of the given triangle is 4.5 sq units.