Can you find the area of the triangle shown?

The area of the triangle is equal to the area of the rectangle circumscribing the triangle minus the sum of the areas of the three small triangles. We have

$A=10(12)-\dfrac{1}{2}[8(12)+2(8)+10(4)]=120-\dfrac{1}{2}(152)=\boxed{44}$

To simplify the arithmetic, consider the lower left vertex to be at $(0,0)$ , then apply the Shoelace Formula.

$Area = \frac{1}{2}det\left({\begin{array}{ccc} 0 & 0 & 1 \\ 10 & 4 & 1 \\ 8 & 12 & 1 \end{array}}\right)$

$Area = \frac{1}{2}[12(10)-8(4)] = \frac{1}{2}[88] = \fbox{44}$