Area of triangle = $\frac{1}{2}|20(8 - 0) + 0(0 - 10) + 7(10 - 8)| = \frac{174}{2} = 87$

Alternate Approach:

Draw lines CD and CE (as shown in the figure)

Area of triangle ABC = Area of rectangle ODCE - Area of triangle AOB - Area of triangle BDC - Area of triangle CEA

= $(20)(10) - \frac{1}{2}(7)(8) - \frac{1}{2}(13)(10) - \frac{1}{2}(20)(2)$

= $200 - 28 - 65 - 20$
= $87$