So i'm trying to solve this problem without counting the square units in the triangle. So i thought of finding the lengths of RS and ST and find the area of the quadrilateral but since we have a triangle, I would divide by 2.
I found RS to be 6 units and ST to be 12 units, which means the area of the quadrilateral would be 72 units squared and half is 36 units squared. However, that is not a choice and it turns out the right answer is 45 but i can't seem to figure out how they got that answer.
Any ideas?
Best Answer
Another approach: The triangle $RST$ is bounded by a square whose sides have length $12$ and are parallel to the axes. So the triangle can be seen as a square minus three triangles, with corresponding area $$ 12^2 - \frac12(3\cdot 6 + 6\cdot 12 + 9\cdot 12) = 45. $$