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niteshwaghray
GMAT 1: 700 Q45 V40
Posts: 59
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
58% (03:11) correct
42%
(03:04)
wrong
based on 257
sessions
History
Date
Time
Result
Not Attempted Yet
In a rectangular coordinate plane, points A(3,4), B(6,-5), C(-4,-3) and D(-2,2) are joined to form a quadrilateral. What is the area, in square units, of quadrilateral ABCD?
A. 35
B. 37.5
C. 45
D. 52.5
E. 60
A. 35
B. 37.5
C. 45
D. 52.5
E. 60
GMATAspirer09
Well for co=ordinate geometry questions where we have to find area, its better to divide the quadrilateral in rectangles/triangles and find total area.
But in some cases when they are not straight forward and you know the area formula its better to go with formula instead of trying to divide figure in different parts.
In given figure, it's hard to divide quadrilateral internally. In this case we can surround it with a rectangle and subtract the extra part area from total rectangle area.
Please find attached figure for details solution.
Here we have surrounded quadrilateral ABCD externally by rectangle PQRS.
Found total area of PQRS. And subtracted the area of triangles( AQR, CSR, XDC and YDA) and square (PYXD)for formed outside it.
Answer: D
Well for co=ordinate geometry questions where we have to find area, its better to divide the quadrilateral in rectangles/triangles and find total area.
But in some cases when they are not straight forward and you know the area formula its better to go with formula instead of trying to divide figure in different parts.
In given figure, it's hard to divide quadrilateral internally. In this case we can surround it with a rectangle and subtract the extra part area from total rectangle area.
Please find attached figure for details solution.
Here we have surrounded quadrilateral ABCD externally by rectangle PQRS.
Found total area of PQRS. And subtracted the area of triangles( AQR, CSR, XDC and YDA) and square (PYXD)for formed outside it.
Answer: D
Attachments
Area of Quadrilateral.jpg [ 1.73 MiB | Viewed 10846 times ]
Given data
x1=3,y1=4
x2=6,y2=-5
x3=-4,y3=-3
x4=-2,y4=2
Given the vertices of the quadrilateral
Area = \(\frac{1}{2} *| (x1y2 - y1x2) + (x2y3 - y2x3) + (x3y4 - y3x4) + (x4y1 - y4x1) |\)
Substituting these values,
Area = \(\frac{1}{2} * | -38 -39 -14 -14|\) = \(\frac{1}{2} * | -105|\) = 52.5(since absolute value of -105 is 105) (Option D)
x1=3,y1=4
x2=6,y2=-5
x3=-4,y3=-3
x4=-2,y4=2
Given the vertices of the quadrilateral
Area = \(\frac{1}{2} *| (x1y2 - y1x2) + (x2y3 - y2x3) + (x3y4 - y3x4) + (x4y1 - y4x1) |\)
Substituting these values,
Area = \(\frac{1}{2} * | -38 -39 -14 -14|\) = \(\frac{1}{2} * | -105|\) = 52.5(since absolute value of -105 is 105) (Option D)
General Discussion
Posts: 12
pushpitkc
Formulas are a big NO NO for GMAT.
pushpitkc can you please suggest some other method to do this question?
shettytarun
Joined: 18 Sep 2009
Last visit: 15 Apr 2018
Posts: 11
Location: India
WE:Business Development (Internet and New Media)
Posts: 11
pushpitkc
Hi pushpitkc
can you please elaborate on the what principle you have used to solve this question, I havent come across the formula used by you
Nikkb
hi, my solution is exact xerox copy of yours, kudos to you!!
Thanks pushpitkc for formula, saves lot of time.
Posts: 28
hellosanthosh2k2
Thanks for the diagram - any way to do this in under 3mins? I see avg time of 17 mins..
Posts: 3
pushpitkc
Did some googling, and found out that the name of the formula used was the "shoelace formula". Basically, its a formula that allows you to calculate the area of a quadrilateral if you have all the vertices.
An easier version to remember of this formula would be
Area = \(\frac{1}{2} *| x1y2 + x2y3 + x3y4 + x4y1 - y1x2 - y2x3 - y3x4 - y4x1 |\)
Thanks for helping people with the name, blazeowlss
I had studied it in school and didn't really remember the name
I had studied it in school and didn't really remember the name
(d1xd2)/2
d1 is diagonal AC
d2 is diagonal BD
Ans. is "D".
Please correct if I am wrong.
d1 is diagonal AC
d2 is diagonal BD
Ans. is "D".
Please correct if I am wrong.
rahul16singh28
Joined: 31 Jul 2017
Last visit: 09 Jun 2020
Posts: 428
Location: Malaysia
Schools: INSEAD Jan '19
GPA: 3.95
WE:Consulting (Energy)
Schools: INSEAD Jan '19
Posts: 428
niteshwaghray
The Area of Triangle with \(A(x1,y1) B(x2,y2) C(x3,y3)\) = \(\frac{1}{2}|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)\)|. Now, Divide the Quadrilateral in two triangles and find the area using the formula. Hence, D.
gvij2017
That is the formula for the rombus. This is not a rombus. According to that formula, the answer is 49.0025.
_________________
Clipper Ledgard
GMAT Coach
GMAT Coach
Posts: 1,324
Great method, it is certainly one I will use in future questions.
Was anyone able to get this question done in under 3 to 3 and half minutes?
I just about made it under 4 minutes using this method....
Was anyone able to get this question done in under 3 to 3 and half minutes?
I just about made it under 4 minutes using this method....
Nikkb
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