Area

A systematic way to find area from given coordinates is summation of area under the straight line between two adjacent coordinates in a loop. First arrange the $n$ pairs of coordinates enclosing the area in a clockwise order. Let the first pair of coordinates be the $(n+1)$ th pair to close the loop, that is $(x_1, y_1) = (x_{n+1}, y_{n+1})$ .

$\begin{aligned} A & = \sum_{k=1}^4 \frac {(y_{k+1}+y_k)(x_{k+1}-x_k)}2 \\ & = \frac {(6+5)(6-1)}2 + \frac {(2+6)(7-6)}2 + \frac {(2+2)(3-7)}2 + \frac {(5+2)(1-3)}2 \\ & = \frac {55}2 + \frac {8}2 + \frac {-16}2 + \frac {-14}2 \\ & = \boxed{\dfrac {33}2} \end{aligned}$