Hi Mike,
question on Math Quiz 4 #9: I get the answer and the proposed solution (area of large triangle minus area of small triangle). But my daughter worked the problem differently and I think what she did was correct, but she got a slightly different answer and I can’t figure out exactly why.
Her solution: she used Pythag Theorem to get the hypot of small triangle: so 4^2 + 1^2 = c^2…. so c=Sqrt(17). This is base of large triangle. So A= 1/2 bXh, or 1/2 (sqrt 17)(8), she got 16.492.

When you’re finding the area of a triangle, the height you use needs to be perpendicular to the base you choose. In this case, drawing a segment from (2, 6) that is perpendicular to that base would require drawing it outside of the triangle.

If you’re going to use as your base (segment BC), then you need to use segment AD in the figure above as your height. This can be done easily with software, but I wouldn’t advise trying to do it by hand on test day.