$\triangle OPQ$ is formed by th

e coordinates $P(0,\,5),\, Q(8,\,0)$ and origin $O$.

The area of $\triangle OPQ$ is ____ square units.

We know that the area of the triangle whose vertices are $\displaystyle (x_{1},y_{1}),(x_{2},y_{2}),$ and $(x_{3},y_{3})$ is $\cfrac{1}{2}\left | x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1}) +x_{3}(y_{1}-y_{2})\right |$

Area of $\triangle OPQ$

$=\dfrac 12 \left[ 1(0) - 1(0) +1(-40)\right]$

$=\dfrac 12 \times 40 = 20$ sq. units