Shoelace formula: you take the x-coordinates of all of the points and write them down, vertically, in order (clockwise or counter) until you write the first number twice. You do the same with the y-coordinates, next to the first list. Then, you multiply the x-coordinate to the y-coordinate that is one down, which makes a shoelace-like formation. Finally, you add all of the numbers on the left and right, find the difference, then divide the absolute value of that by 2.
#1
-1 4
2 2
2 -2
-2 -4
-5 -2
-5 2
-1 5
Left products: 8, 4, 4, 20, 10, -2
Right products: -2, -4, -8, 4, -10, -25
Sums: 44, -45
AV of Difference: 89
Area = 44.5 units²
#2
-1 2
1 5
3 2
3 -1
-5 -3
-5 2
-3 5
Left products: 2, 15, 6, 5, 15, -6
Right products: -5, 2, -3, -9, -10, -25
Sums: 37, -50
AV of difference: 87
Area = 43.5 units²
