Hello, fabxx!

Did you make a sketch?

In rectangle ABCD, point E is the midpoint of line segment BC.

If the area of $\displaystyle ABED$ is $\displaystyle \frac{2}{3}$, what is the area of $\displaystyle ABCD$?

$\displaystyle (a)\;\frac{1}{2} \qquad(b)\;\frac{3}{4}\qquad (c)\;\frac{8}{9} \qquad (d)\;1 \qquad (e) \;\frac{8}{3}$ Code:

D *---------------* C
| * |
| * |
| * |
F * - - - - - - - * E
| |
| |
| |
A *---------------* B

Draw median EF.

$\displaystyle \text{Rect }DCEF \:=\:\frac{1}{2}(\text{Rect }ABCD) $

$\displaystyle \Delta DCE \:=\:\frac{1}{2}(\text{Rect }DCEF) \;=\;\frac{1}{4}(\text{Rect }ABCD)$

. . Hence: .$\displaystyle \text{Quad }ABED \:=\:\frac{3}{4}(\text{Rect }ABCD) $

We are told that: .$\displaystyle \text{Quad }ABED \:=\:\frac{2}{3}$

We have: .$\displaystyle \frac{3}{4}(\text{Rect }ABCD) \;=\;\frac{2}{3} \quad\Rightarrow\quad \boxed{\text{Rect }ABCD \:=\:\frac{8}{9}}$ . . . answer (c)