What is the area of the triangle formed by

The given triangle $\Delta \mathrm{OAB}$ is a right angled triangle, right angled at $O$. the co-ordinates of the vertices are $O(0,0) A(6,0)$ and $B(0,4)$.

So,

Altitude is 6 units and base is 4 units.

Therefore,

$\operatorname{ar}(\Delta \mathrm{OAB})=\frac{1}{2}($ Base $)($ Altitude $)$

$=\frac{1}{2}(4)(6)$ sq. units

$=12$ sq. units