A quadrilateral has vertices, taken in order, at (1, 1), (7, −3), (12, 2) and (7, 21). What is its area?

Split it along the diagonal from (1, 1) to (12, 2). Triangle (1,1),(7,−3),(12,2) has area ½|1(−3 − 2) + 7(2 − 1) + 12(1 + 3)| = ½|−5 + 7 + 48| = 25. Triangle (1,1),(12,2),(7,21) has area ½|1(2 − 21) + 12(21 − 1) + 7(1 − 2)| = ½|−19 + 240 − 7| = 107. Total = 25 + 107 = 132 square units. Forgetting the factor ½ gives 264.