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What is the area of the quadrilateral with vertices A, B, C, and D?

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Intern
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Joined: 16 Nov 2016
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Concentration: International Business, Marketing
What is the area of the quadrilateral with vertices A, B, C, and D?  [#permalink]

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New post 17 Aug 2019, 14:28
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A
B
C
D
E

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What is the area of the quadrilateral with vertices A, B, C, and D?
(1) The perimeter of ABCD is equal to 16.
(2) Quadrilateral ABCD is a square.
Senior Manager
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Joined: 18 May 2019
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Re: What is the area of the quadrilateral with vertices A, B, C, and D?  [#permalink]

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New post 17 Aug 2019, 15:47
1. A quadrilateral is a 4 sided figure. It can be square, a trapezoid, rectangle, parallelogram, etc. So, knowing the perimeter is not enough to determine the Area. Statement 1 is therefore insufficient.

2. Knowing that the quadrilateral ABCD is a square alone is not sufficient. We need to know the length of the sides of the square otherwise we can have endless possibilities resulting in many Areas of the quadrilateral.

Combining 1 and 2 is however sufficient since we can determine the length of each side of the square from the perimeter which was given as 16.
Perimeter of a square = l+l+l+l = 4l
So 4l=36 meaning l =4.
Area of ABCD = 4*4 =16. Therefore statement and 1 and 2 taken together are sufficient. Answer is therefore C.

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Re: What is the area of the quadrilateral with vertices A, B, C, and D?   [#permalink] 17 Aug 2019, 15:47
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What is the area of the quadrilateral with vertices A, B, C, and D?

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