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ManHattan Problem

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ManHattan Problem

by kakz » Tue Nov 15, 2011 2:51 am
Sides AB, BC, and CD of quadrilateral ABCD all have length 10. What is the area of quadrilateral ABCD?

(1) BC is parallel to AD.
(2) Diagonal AC, which lies inside the quadrilateral, has length 10√3.
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by neelgandham » Tue Nov 15, 2011 3:32 am
Sides AB, BC, and CD of quadrilateral ABCD all have length 10. What is the area of quadrilateral ABCD?
(1) BC is parallel to AD.
The resulting quadrilateral ABCD can be a sqaure or a rhombus or an Isosceles Trapezoid (refer attachment).So, it is not possible to find the area without knowing the angle between the sides or without knowing the shape and type of the quadrilateral.

Insufficient !
(2) Diagonal AC, which lies inside the quadrilateral, has length 10√3.
Again insufficient, because it doesn't give any information about the length of side AD or information regarding the shape of the quadrilateral!
From 1 and 2
If the quadrilateral is a Rhombus then the area = 100
If the quadrilateral is an Isosceles Trapezoid = 100 + x (need not to calculate)
Note: The quadrilateral can not be a square

Two different values! IMO Option E

Correct me if I am wrong!
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by GMATGuruNY » Tue Nov 15, 2011 1:11 pm
kakz wrote:Sides AB, BC, and CD of quadrilateral ABCD all have length 10. What is the area of quadrilateral ABCD?

(1) BC is parallel to AD.
(2) Diagonal AC, which lies inside the quadrilateral, has length 10√3.
Don't calculate. DRAW.
The following figures -- each with a different area -- satisfy both statements:

Image

The correct answer is E.
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