BTGmoderatorDC wrote:What is the area of the quadrilateral with vertices A, B, C, and D?
(1) The perimeter of ABCD is equal to 16.
(2) Quadrilateral ABCD is a rhombus.
Source: Manhattan Prep
\[? = {S_{ABCD}}\]
Let´s BIFURCATE statements (1) and (2) together, so that we prove the correct answer is (E).
\[\left( {1 + 2} \right)\,\,4x = 16\,\,\, \Rightarrow \,\,\,x = 4\,\,\,\left( {{\text{each}}\,\,{\text{side}}\,\,{\text{length}}} \right)\]
Note that a square with edge 4 has an area of 16, while the other rhombus (shown in the right) has an area different from 16.
(A careful reader realizes it is possible to have an area as small as we wish, I mean, positive but as near as 0 as desired!)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
