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.
OA E
Source: Manhattan Prep
What is the area of the quadrilateral with vertices A, B, C,
This topic has expert replies
-
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
- fskilnik@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
\[? = {S_{ABCD}}\]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
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.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br