given points are (0,0) , (2,4) and (4,2)

formula for finding the distance between 2 coordinates is ((x1-x2)^2 + (y1-y2)^2)^0.5

it is clear that the distance between (0,0) and (2,4) is the same as (0,0) and (4,2)
so ((2^2) + (4^2))^0.5 = 2√5

distance between (2,4) and (4,2) is easier and would result in 2√2

so not, we can see that it is an isosceles triangle with the base of 2√2

formula for the area of triangle is 0.5 * B * H , B for base length and H for height

we know B but not H

imagine a perpendicular line from the base, you can see that it pass through the origin so therefore we can use Pythagoras theorem

x^2 + y^2 = z^2
if we choose x as unknown y as half base length because the line we imagined passes through the middle of the base and z as 2√5,
we see that x^2 + 2 = 20
so x = 3√2

area of the triangle = 0.5 * 2√2 * 3√2 = 6

option B is the right answer