The area of triangle OAB with O(0,0), A(4,0), and B(0,6) is:

The formula to find the area of a triangle given the coordinates of its vertices is:

Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|

Plugging in the coordinates of the vertices O(0,0), A(4,0), and B(0,6):

Area = 1/2 * |0(0 - 6) + 4(6) + 0(0 - 0)|
Area = 1/2 * |0 - 24 + 0|
Area = 1/2 * |-24|
Area = 1/2 * 24
Area = 12

Therefore, the area of triangle OAB is 12 square units.

The area of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3) can be calculated using the determinant formula:

Area = 0.5 - |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|

Using the given vertices, we can plug in the values:

Area = 0.5 - |0(0 - 6) + 4(6 - 0) + 0(0 - 0)|
Area = 0.5 - |0 + 24 + 0|
Area = 0.5 - |24|
Area = 12 square units

Therefore, the area of triangle OAB is 12 square units.