Source MGMAT CAT 2
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
I could sense that in explanation provided by MGMAT guys on test is that
When we combine both st1 and st2 , we have a rhombus with sides 4 each
Now the Area of rhombus can be ( 4 * 4 ) = 16
OR
The area of Rhombus can be ( Base * Height = 4 * 2 root3 )
So, are they considering Rhombus to be a Parallelogram ?? qestion 1
FACT : I knew that Area of Rhombus = .5 * diagonal1 * diagonal 2.. This is something new I learnt..
Is every Square a Rectangle ?
Is everry Rhombus a Parallelogram?
What Am I missing here ??[/spoiler]
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Rhombus / Parallelogram ?
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Stuart@KaplanGMAT
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The OA is correct.mmslf75 wrote:Source MGMAT CAT 2
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
I could sense that in explanation provided by MGMAT guys on test is that
When we combine both st1 and st2 , we have a rhombus with sides 4 each
Now the Area of rhombus can be ( 4 * 4 ) = 16
OR
The area of Rhombus can be ( Base * Height = 4 * 2 root3 )
So, are they considering Rhombus to be a Parallelogram ?? qestion 1
FACT : I knew that Area of Rhombus = .5 * diagonal1 * diagonal 2.. This is something new I learnt..
Is every Square a Rectangle ?
Is everry Rhombus a Parallelogram?
What Am I missing here ??[/spoiler]
Special shapes also belong to general categories.
Every square is a rhombus, rectangle, parallelogram and quadrilateral.
Every rectangle is a parallelogram and quadrilateral.
Every rhombus is a parallelogram and quadrilateral.
Every parallelogram is a quadrilateral.
Basically, if a shape fits the definition of a more general shape, it also belongs to that class. Since a parallelogram is simply a quadrilateral with 2 pairs of parallel sides, and since squares, rectangles and rhombii all have 2 pairs of parallel sides, they're all parallelograms.
The formula for the area of a parallelogram is simply:
area = base * height
Combining the statements, we know that we have a parallelogram with sides of 4 (by definition a rhombus has 4 equal sides, so we calculate the length of a side by taking perimiter/4); however, we have no clue how "slanted" the rhombus is, so there's no way to calculate the height. For example, the shape could be a square with an area of 16 or could have any area smaller than 16, depending on the angles.
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mmslf75
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In MGMAT explanation it is assumed ABCD to be a ll gram...with angle 60 degrees...therefore height 2 root 3punitkaur wrote:Hi mmslf75,
how did you calculate the height of the rhombus given the side?
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Is it assumed that the angle is 60 degrees, or is that just given as one possibility, in order to show that the statements are insufficient?mmslf75 wrote:In MGMAT explanation it is assumed ABCD to be a ll gram...with angle 60 degrees...therefore height 2 root 3punitkaur wrote:Hi mmslf75,
how did you calculate the height of the rhombus given the side?
As I stated in my post above, a rhombus is a sub-class of parallelogram.
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mmslf75
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Stuart Kovinsky wrote:Is it assumed that the angle is 60 degrees, or is that just given as one possibility, in order to show that the statements are insufficient?mmslf75 wrote:In MGMAT explanation it is assumed ABCD to be a ll gram...with angle 60 degrees...therefore height 2 root 3punitkaur wrote:Hi mmslf75,
how did you calculate the height of the rhombus given the side?
As I stated in my post above, a rhombus is a sub-class of parallelogram.
Assumed 60 degrees..
I actually went by my own theory that since we are asked to find area of rhombus, I can say area = .5 d1 d2 and since d1 and d2 are not possible..to find out....I marked E
but u explained with the other concept..Do we actually need to go that far ?
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mmslf75
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mmslf75 wrote:Stuart Kovinsky wrote:Is it assumed that the angle is 60 degrees, or is that just given as one possibility, in order to show that the statements are insufficient?mmslf75 wrote:In MGMAT explanation it is assumed ABCD to be a ll gram...with angle 60 degrees...therefore height 2 root 3punitkaur wrote:Hi mmslf75,
how did you calculate the height of the rhombus given the side?
As I stated in my post above, a rhombus is a sub-class of parallelogram Assumed 60 degrees..
I actually went by my own theory that since we are asked to find area of rhombus, I can say area = .5 d1 d2 and since d1 and d2 are not possible..to find out....I marked E
but u explained with the other concept..Do we actually need to go that far ?
think I understand now..
IN GENERAL AREA OF A PARALLELO is BASE * HEIGHT ( and PARALLELO being the SUPERSET of ALL QUADS ) we took
the area of rhombus to be the same
Wow !! I got it
thanks
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agarwalmanoj2000
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Should answer be C? Please advise.
- Area of Rhombus = (D1*D2)/2
- 2 diagonals of Rhombus are equal and perpendicular bisector.
Based on statement 1 & 2, each side of the Rhombus is 4. As the diagonals are perpendicular bisector, they bisect each other making 90 degree angle. Diagonals makes 4 isosceles right angle triangle with hypotenuse equal to 4, so the other sides of each triangle will be 4/Sq.root 2 and hence diagonals will equal 2*(4/Sq.root 2) = 8/Sq.root 2.
Therefore area of the Rhombus = [(8/Sq.root 2) * (8/Sq.root 2)] *2 = 64.
- Area of Rhombus = (D1*D2)/2
- 2 diagonals of Rhombus are equal and perpendicular bisector.
Based on statement 1 & 2, each side of the Rhombus is 4. As the diagonals are perpendicular bisector, they bisect each other making 90 degree angle. Diagonals makes 4 isosceles right angle triangle with hypotenuse equal to 4, so the other sides of each triangle will be 4/Sq.root 2 and hence diagonals will equal 2*(4/Sq.root 2) = 8/Sq.root 2.
Therefore area of the Rhombus = [(8/Sq.root 2) * (8/Sq.root 2)] *2 = 64.
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newgmattest
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Please remember that diagonals of Rhombus are *NOT* equal in length and they just bisect the other at 90 degree.
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amit2k9
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a+b
base = 4 but height = ?
E it is.
base = 4 but height = ?
E it is.
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gmattesttaker2
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Hello,
I was trying to solve as follows:
1 - Insuff. Since we don't know what kind of quadrilateral it is.
2 - Insuff. No information about rhombus ABCD. Hence, can't calculate area.
1 and 2:
Perimeter of rhombus ABCD = 16. Hence, each side is 4 (since all sides are equal).
Area of rhombus = 1/2 * (d1 + d2) , where d1 and d2 are diagonals of the rhombus
However, I was not sure after this point. Can you please tell what information is needed to find the diagonals of a rhombus? Thanks a lot.
Best Regards,
Sri
I was trying to solve as follows:
1 - Insuff. Since we don't know what kind of quadrilateral it is.
2 - Insuff. No information about rhombus ABCD. Hence, can't calculate area.
1 and 2:
Perimeter of rhombus ABCD = 16. Hence, each side is 4 (since all sides are equal).
Area of rhombus = 1/2 * (d1 + d2) , where d1 and d2 are diagonals of the rhombus
However, I was not sure after this point. Can you please tell what information is needed to find the diagonals of a rhombus? Thanks a lot.
Best Regards,
Sri
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theCodeToGMAT
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At this point, we cannot calculate the measure of Diagnol.. had this question mentioned that, side angles are 90*.. then we could have move forward..gmattesttaker2 wrote:Hello,
I was trying to solve as follows:
1 - Insuff. Since we don't know what kind of quadrilateral it is.
2 - Insuff. No information about rhombus ABCD. Hence, can't calculate area.
1 and 2:
Perimeter of rhombus ABCD = 16. Hence, each side is 4 (since all sides are equal).
Area of rhombus = 1/2 * (d1 + d2) , where d1 and d2 are diagonals of the rhombus
However, I was not sure after this point. Can you please tell what information is needed to find the diagonals of a rhombus? Thanks a lot.
Best Regards,
Sri
So [spoiler]{E}[/spoiler]
R A H U L
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When the statements are combined, ABCD could look like either of the following:mmslf75 wrote:Source MGMAT CAT 2
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.
Case 1:
Case 2:
Thus, different areas are possible.
The correct answer is E.
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As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
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Anaira Mitch
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Just curious to know if in statement 2 it would have been "(2) Quadrilateral ABCD is a Square". I believe answer should have been C.
Anyone can confirm on this?
Anyone can confirm on this?
