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# What is the total area of the figure, if the area of the shaded region

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
What is the total area of the figure, if the area of the shaded region  [#permalink]

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05 Sep 2018, 22:38
00:00

Difficulty:

55% (hard)

Question Stats:

63% (01:46) correct 37% (02:04) wrong based on 55 sessions

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What is the total area of the figure, if the area of the shaded region is 100 and MK = 10?

(1) x = y = 45
(2) QL = 10

Attachment:

image008.jpg [ 4.4 KiB | Viewed 763 times ]

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Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 958
WE: Supply Chain Management (Energy and Utilities)
What is the total area of the figure, if the area of the shaded region  [#permalink]

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Updated on: 06 Sep 2018, 09:26
Bunuel wrote:

What is the total area of the figure, if the area of the shaded region is 100 and MK = 10?

(1) x = y = 45
(2) QL = 10

Attachment:
The attachment image008.jpg is no longer available

Question stem:- What is the area of the quadrilateral KMNL?

St1:- x = y = 45

Refer the enclosed diagram, $$\triangle{NQL}$$, $$\triangle{KPO}$$, and $$\triangle{KMP}$$ are isosceles right angled triangles(45-45-90) form. sides are in the ratio $$x:x:\sqrt{2}x$$
So base=height=10 and hypotenuse=$$10\sqrt{2}$$

Hence area of $$\triangle{NQL}$$=Area of $$\triangle{KPO}$$=Area of $$\triangle{KMP}$$ (Base and height are known, area can be determined)

Total area of figure=Area of shaded region(100)+3*Area of triangle NQL
Sufficient.

St-2:- QL = 10
Area of the figure will be different at different measures of x.
Insufficient.

Ans. (D)
Edit: Fixed typo. Ans. (A)

Attachments

Area.JPG [ 17.05 KiB | Viewed 640 times ]

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PKN

Rise above the storm, you will find the sunshine

Originally posted by PKN on 06 Sep 2018, 05:47.
Last edited by PKN on 06 Sep 2018, 09:26, edited 1 time in total.
Senior Manager
Joined: 08 Aug 2017
Posts: 325
Re: What is the total area of the figure, if the area of the shaded region  [#permalink]

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06 Sep 2018, 07:45
Hi,

I think lot of assumption are made while solving this problem.
2. KL is parallel to MN

Question stem says nothing about above assumptions.
Can I make such assumptions while solving DS problems.
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 958
WE: Supply Chain Management (Energy and Utilities)
What is the total area of the figure, if the area of the shaded region  [#permalink]

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06 Sep 2018, 08:49
gvij2017 wrote:
Hi,

I think lot of assumption are made while solving this problem.
2. KL is parallel to MN

Question stem says nothing about above assumptions.
Can I make such assumptions while solving DS problems.

Hi gvij2017,

1. Shaded region is square.- we needn't to know the type of quadrilateral it is. We have to find the area of the triangles, add the area of shaded region to get the area of total figure.
2. KL is parallel to MN:- a) KM is perpendicular to MN b)PO perpendicular to KL c) NQ perpendicular to KL ,Hence KL || MN

_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Joined: 18 Jun 2018
Posts: 116
Location: United States (AZ)
Concentration: Finance, Healthcare
GPA: 3.86
Re: What is the total area of the figure, if the area of the shaded region  [#permalink]

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06 Sep 2018, 09:07
1
You said st 2 is insufficient and still picked D as the correct answer? PKN

PKN wrote:
gvij2017 wrote:
Hi,

I think lot of assumption are made while solving this problem.
2. KL is parallel to MN

Question stem says nothing about above assumptions.
Can I make such assumptions while solving DS problems.

Hi gvij2017,

1. Shaded region is square.- we needn't to know the type of quadrilateral it is. We have to find the area of the triangles, add the area of shaded region to get the area of total figure.
2. KL is parallel to MN:- a) KM is perpendicular to MN b)PO perpendicular to KL c) NQ perpendicular to KL ,Hence KL || MN

Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 958
WE: Supply Chain Management (Energy and Utilities)
What is the total area of the figure, if the area of the shaded region  [#permalink]

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06 Sep 2018, 09:20
funsogu wrote:
You said st 2 is insufficient and still picked D as the correct answer? PKN

PKN wrote:
gvij2017 wrote:
Hi,

I think lot of assumption are made while solving this problem.
2. KL is parallel to MN

Question stem says nothing about above assumptions.
Can I make such assumptions while solving DS problems.

Hi gvij2017,

1. Shaded region is square.- we needn't to know the type of quadrilateral it is. We have to find the area of the triangles, add the area of shaded region to get the area of total figure.
2. KL is parallel to MN:- a) KM is perpendicular to MN b)PO perpendicular to KL c) NQ perpendicular to KL ,Hence KL || MN

Hi funsogu,
You have pointed it out correctly. My bad ,how did I write D? It is A. Need to fix typo error.

Posted from my mobile device
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Intern
Joined: 07 Sep 2018
Posts: 4
Re: What is the total area of the figure, if the area of the shaded region  [#permalink]

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07 Sep 2018, 02:34
KM and QN are both perpendicular to the same lines. Therefore they are parallel to each other by the property of parallel lines. so the figure KMQN forms a parallelogram with two adjacent angles 90 degree, which means it is a rectangle. also the adjacent sides are 10. so the figure forms a square.
Re: What is the total area of the figure, if the area of the shaded region   [#permalink] 07 Sep 2018, 02:34
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