Answer:
c.
Explanation:
I go a slightly different route than the other answer.
let's see the side lengths of the triangle :
AB² = (7-4)² + (2-4)² = 3² + (-2)² = 9 + 4 = 13
AB = sqrt(13)
BC² = (1-7)² + (2-2)² = (-6)² + 0² = 36
BC = 6
CA² = (4-1)² + (4-2)² = 3² + 2² = 9 + 4 = 13
CA = sqrt(13)
it is an isoceles triangle (the legs have the same length).
so, we get the height via Pythagoras (for the right-angled triangle with height and BC/2 as legs) :
CA² = height² + (BC/2)²
13 = height² + 3² = height² + 9
height² = 4
height = 2
and the area of the triangle is then (baseline×height/2) :
6×2 / 2
and that is half of the area of a 6×2 rectangle.