Question

I was told the answer is D but not sure why. How do I figure it out?

Answer 1

Check the picture below.

the area of the region in white, is really the area of a trapezoid that has a height = 2, and bases of 3 and 6, so let's get its area

`\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h=height\\ a,b=\stackrel{parallel~sides}{bases}\\[-0.5em] \hrulefill\\ h=2\\ a=3\\ b=6 \end{cases}\implies A=\cfrac{2(3+6)}{2}\implies A=9`

now that we know the area in white, let's check all expressions, and whichever does NOT result in 9, is it.

`\boxed{A}\qquad (2)(6)-\cfrac{1}{2}(2)(3)\implies 12-3\implies 9 \\\\\\ \boxed{B}\qquad (4)(6)-\cfrac{1}{2}(4)(3)-2(3)-\cfrac{1}{2}(3)(2)\implies 24-6-6-3\implies 9 \\\\\\ \boxed{C}\qquad (3)(2)+\cfrac{1}{2}(3)(2)\implies 6+3\implies 9 \\\\\\ \boxed{D}\qquad (6)(2)+\cfrac{1}{2}(3)(4)\implies 12+6\implies 18\qquad \textit{\Large \checkmark}`