The area of a triangle is
A = (1/2)bh
b, the base is found by using the distance formula with (0,2) and (4,2):
d = SQR[(4 - 0)^2 - (2 - 2)^2] = 4
b = 4
The height, h, is the y-difference between (3,7) and the line segment formed by the other two points.
h = 5
Area = (1/2)(4)(5) = 10