GRE Sample Test 1 Quantitative Reasoning 2

Plug In! To find the area of quadrilateral ABDE, find the area of right ΔABC and subtract the area of right ΔEDC. Make a = 4 and b = 2. Because AB = BC, you know that this triangle has a height and base that are both equal to 4. The area of ABC is 4 × 4 × $/2$ = 8.
The area of EDC is 2 × 2 × $\frac{1}{2}$ = 2.
The area of ABDE is 8 − 2 = 6. Plug In for a and b and find that (A) is the only one that works.
Alternatively, to find the area of quadrilateral ABDE, find the area of right ΔABC and subtract the area of right ΔEDC. Both the base and the height of ΔABC are a, so the area equals $\frac{1}{2}$ × a × a, or $\frac{{\mathit{a}}^2}{2}$.
Both the base and the height of ΔEDC are b, so the area equals $\frac{1}{2}$ × b × b, or $\frac{{\mathit{b}}^2}{2}$.
Therefore, the area of quadrilateral ABDE is $\frac{{\mathit{a}}^2}{2}-\frac{{\mathit{b}}^2}{2}$.