15 sq. units
Look at the points this way (repeat the first coord pair at the end):
Multiply the numerators by the next following denominator:
0*9 + 0*9 + 6*4 = 24
Then multiply the denominators by the next following numerator:
4*0 + 9*6 + 9*0 = 54
Subtract those two sums & take half:
(54 - 24 )/2 = 15
15 sq. units [that agrees with ukorov]
anyways since you have 2 points alligned on the x - coordinates
(0,4) and (0,9) then the line on that side of the triangle is 5... 9-4 = 5
it happens again with (0,9) and (6,9) ... the line on that side is 6... 6-0 = 6
a triangles area is length times width divided by 2.. or half its base times its height...
6*5 = 30.... 30/2 = 15..
-or-
(0.5)(5)(6) = 15..
15 sq units..