jmc

The vertices of the trapezoid are $(5,5)$, $(10,10)$, $(0,10)$, and $(0,5)$. Its bases are $5$ and $10$ units long, and its height is $5$ units. Averaging the bases and multiplying by the height, we find an area of $\left(\frac{5+10}{2}\right)(5)=\boxed{37.5}$ square units.