Question about "Splitting the Field" condition

OK. I read the problem condition of the problem “Splitting the Field

I found the other answer for sample input. Maybe I stupid. But we can join points

(1; 1), (2; 3), (4; 2), area = 12

and

(8; 10), (9; 12), (14; 7), area = 42

so answer is 42 + 12 = 54

Where I wrong?