In a rectangular coordinate plane, points A(3,4), B(6,-5), C(-4,-3) an

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 = \(\frac{1}{2} *| (x1y2 - y1x2) + (x2y3 - y2x3) + (x3y4 - y3x4) + (x4y1 - y4x1) |\)
Substiuting 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)

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 = \(\frac{1}{2} *| (x1y2 - y1x2) + (x2y3 - y2x3) + (x3y4 - y3x4) + (x4y1 - y4x1) |\)
Substiuting 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)

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

PS: Took help from someone to solve it but not sure of his gmatclub id to tag.

+1 kudos if you like the solution.

hi, my solution is exact xerox copy of yours, kudos to you!!

Thanks pushpitkc for formula, saves lot of time.

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)

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

(d1xd2)/2
d1 is diagonal AC
d2 is diagonal BD

Ans. is "D".
Please correct if I am wrong.

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