BTGmoderatorDC wrote:

ABCD is a quadrilateral as shown in the figure above. Find the area of the quadrilateral.


$$(1)The\ diagonals\ bisect\ each\ other\ at\ 90^o\ \ and\ they\ are\ equal.$$
$$(2)The\ length\ of\ each\ diagonal\ is\ 10cm.$$

OA C

Source: e-GMAT

Let's take each statement one by one.

$$(1)The\ diagonals\ bisect\ each\ other\ at\ 90^o \ and\ they\ are\ equal.$$

Since we do not know the length of diagonals, we can't calculate the area. Insufficient.

$$(2)The\ length\ of\ each\ diagonal\ is\ 10cm.$$

The angle between the diagonals is necessary to ascertain whether the quadrilateral ABCD is a square. If the angle between the diagonals is less than 90º, ABCD would be a rectangle, and then merely by knowing the length of the diagonals, we cannot get the area. Insufficient.

(1) and (2) together

Since from (1), we know that diagonals bisect each other at 90º and the length of each diagonal is 10, ABCD is a square; the length of each side = 10/√2. Thus, area of ABCD = (10/√2)*(10/√2) = 50. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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