Question

Triangle EFG, with vertices E(-9,2), F(-5,3), and G(-7,5), is drawn inside a rectangle, as shown below.

Answer 1

Check the picture below.

so hmmm let's get the whole area of the rectangle, and then get the areas of those 3 triangles and subtract their area from that of the rectangle's, what's leftover is what we didn't subtract, namely, the white triangle.

$\stackrel{\textit{\huge Areas}}{\stackrel{rectangle}{(3)(4)}~~ - ~~\stackrel{green~triangle}{\cfrac{1}{2}(2)(3)}~~ - ~~\stackrel{pink~triangle}{\cfrac{1}{2}(2)(2)}~~ - ~~\stackrel{yellow~triangle}{\cfrac{1}{2}(4)(1)}} \\\\\\ 12~~ - ~~3~~ - ~~2~~ - ~~2\implies 5$