In the diagram above, coordinates are given for three of the vertices

hi rich,
thanks .. you are absolutely correct... i dont know why i took x as the height... a mistake.. kudos for it ... editing the answer in light of this error

The bottom triangle has an area of 16. If the area of the upper triangle is larger or smaller than 14, then we can determine if the area is greater than 30.

Statement 1:
We do not know the y coordinate, it could be any positive number.
Insufficient

Statement 2:
Since it is a parallelogram, the areas of the two triangles must be equal.
Sufficient

Answer: B

MAGOOSH OFFICIAL SOLUTION:

In this problem, the lower triangle ACD has a base of AC = 8, and a height, from the origin down to D, of 4. Therefore, the area of ACD = (1/2)(b)(h) = (1/2)(8)(4) = 16. We would need to know something about the upper triangle ABC to know the answer to the prompt question. We know the base of triangle ABC, AC = 8, but we don’t know anything about the height.

Statement #1: if we know the x-coordinate of point B, that doesn’t help us. We still know the base AC = 8, but we don’t know the height, only the vertical line along which point B will lie. Any height could be possible. This statement, alone and by itself, is insufficient.

Statement #2: the diagonal of any parallelogram (i.e. the line connecting two opposite vertices) divides it into two congruent triangles. Well, if ABCD is a parallelogram, then line AC is a diagonal, which means triangles ADC and ABD must be congruent and have equal area. This would allow us to calculate the total area and answer the prompt question. This statement, alone and by itself, is sufficient.

Answer = B

Hi dkumar2012,

I'm going to give you some hints about how you can go about solving this question, so that you can re-attempt it:

Since the question asks about the relative area of the quadrilateral, you have to figure out a way to calculate if it's greater than 30 (or not).

Notice how the quadrilateral can be broken into 2 triangles (using the X-axis to split it in two). You CAN calculate the area of the "lower" triangle (remember Area = (1/2)(B)(H)). So you really just need to figure out the area of the "upper" triangle. What do you need to know to figure out THAT area....? And do the two Facts provide you with the proper information that you need?

GMAT assassins aren't born, they're made,
Rich

In the diagram, coordinates are given for three of the vertices of quadrilateral ABCD. Does quadrilateral ABCD have an area greater than 30?

Ans: with already given information we know that triangle ABC and ADC are two triangle.
we know the area of triangle ADC is= [AC*OD]*(1/2)= 16
to get the are of Triangle ABC we need to know height of the triangle

(1): point B has an x-coordinate of 4
It does not say anything about the height of triangle ABC. (Insufficient)

(2): quadrilateral ABCD is a parallelogram
as it is parallelogram triangle ABC and ADC are the same triangle. (Properties: diagonal divides equally)
now we know the area of ABCD. we can answer the question. (Sufficient)

Ans:B

Answer B .
Diagonals divided ||gram into two equal halves.
A is insufficient.

Why am I not getting the same result through the area = axb rule for regular quadrilaterals? Through pyth. side CD would be sqrt(52), and AD sqrt(20), which multiplied are 4 x sqrt(65), it would have to be 4 x sqrt(64) for it to give the same answer (32).

Hi,

I was wondering if this system of thought/analysis would hold good for the same problem had Statement 2 were to be changed to say: "quadrilateral ABCD is a rectangle"?

Thanks

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