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# If the perimeter of quadrilateral ABCD is 4, what is its area?

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Manager
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If the perimeter of quadrilateral ABCD is 4, what is its area?  [#permalink]

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Updated on: 09 Dec 2014, 07:00
4
00:00

Difficulty:

45% (medium)

Question Stats:

60% (01:03) correct 40% (00:52) wrong based on 227 sessions

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If the perimeter of quadrilateral ABCD is 4, what is its area?

(1) All four sides of ABCD are of equal length.

(2) All four internal angles of ABCD are right angles.

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aimtoteach

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Originally posted by aimtoteach on 09 Dec 2014, 06:58.
Last edited by Bunuel on 09 Dec 2014, 07:00, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If the perimeter of quadrilateral ABCD is 4, what is its area?  [#permalink]

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09 Dec 2014, 07:05
4
1
If the perimeter of quadrilateral ABCD is 4, what is its area?

(1) All four sides of ABCD are of equal length --> this implies that ABCD is a square (area = 1) or a rhombus (area < 1). Not sufficient.

(2) All four internal angles of ABCD are right angles --> this implies that ABCD is a square (area = 1) or a rectangle. Not sufficient.

(1)+(2) ABCD is a square --> the area = 1. Sufficient.

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Manager
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Re: If the perimeter of quadrilateral ABCD is 4, what is its area?  [#permalink]

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09 Dec 2014, 07:13
Thank you Bunuel for the explanation!

I will make sure to post the questions correctly.
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aimtoteach

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Re: If the perimeter of quadrilateral ABCD is 4, what is its area?  [#permalink]

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14 Mar 2017, 18:03
If the perimeter of quadrilateral ABCD is 4, what is its area?

(1) All four sides of ABCD are of equal length.

(2) All four internal angles of ABCD are right angles.

This question asks us to calculate the area of ABCD; though, we must know what type of quadrilateral ABCD is in order to calculate the area as different quadrilaterals have different formulas for calculating the area.

Statement (1) tells us that all four sides of ABCD are equal in length; however, this is a trap answer because if we divide the area by 4 then we have only have the side lengths. We have to also know that this quadrilateral and cannot assume quadrilateral is a square. Insufficient.

Statement (2) tells us that all the interior angles are right angles, however, this property does not exclusively apply to rectangles- in other words, the quadrilateral could also be a rhombus.
Insufficient.

Statement (1) and Statement (2) still do no provide enough information as we cannot discern whether the shape is a rhombus or rectangle.
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Re: If the perimeter of quadrilateral ABCD is 4, what is its area?  [#permalink]

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15 Mar 2017, 03:32
perimeter is 4

St 1: all sides equal. hence length of one side = 1. the figure could be square or rhombus. Hence area CANNOT BE DETERMINED.
St 2: all angles are equal. it could be a square or rectangle. hence we can say that l +b =2. INSUFFICIENT

St 1 & St 2. we can say that it is a square. hence the area will be 1*1 =1. ANSWER

option C
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Re: If the perimeter of quadrilateral ABCD is 4, what is its area?  [#permalink]

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15 Aug 2018, 00:49
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Re: If the perimeter of quadrilateral ABCD is 4, what is its area?   [#permalink] 15 Aug 2018, 00:49
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