"What is the area? You should be able to solve this"

[Albert Chan]

Another way, still using coordinate geometry, but without Shoelace formula:

Again, let A=(0,2), P=(x,y), B=(2,0)

just sum the area like integration with trapezoid rule:

bottom right area (3 points A, P, B)
= (2+y)/2 * (x-0) + (y+0)/2 * (2-x)
= 1/2 * (2x + x y + 2y - x y)
= x + y

it match the cordinate triangle area formula, without the magic.
it is super easy messing up the "shoelace"

Edit: just realized ijabott just said that in previous post. Sorry for the noise ...