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What is the area of the region in which squares ABCD and EFGH overlap?

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What is the area of the region in which squares ABCD and EFGH overlap?  [#permalink]

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New post 04 Dec 2019, 02:42
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58% (01:22) correct 42% (01:48) wrong based on 53 sessions

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What is the area of the region in which squares ABCD and EFGH overlap?

(1) EF bisects BC.

(2) The distance from point C to point E is \(2\sqrt{2}\) and the distance from point C to point F is \(2\sqrt{2}\).


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Re: What is the area of the region in which squares ABCD and EFGH overlap?  [#permalink]

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New post 04 Dec 2019, 12:50
Tricky one!!

Statement 1- Length of OC =2 cm

But length of OE can vary. (see the figure below for statement 1)

Insufficient

Statement 2-

Case 1- When AB is parallel to EF

OEKC is a square with sides 2cm

Area= 4cm^2

Case 2- When AB is not parallel to EF

Draw perpendicular CJ and CI on EF and EH respectively

CJ=CI=2cm
Angle ICL= Angle JCK

Hence triangle LIC is congruent to triangle KJC. Both triangles have equal areas

Overlapped area EKCL= Area of JCIE= 2*2=4cm^2

Sufficient

B



Bunuel wrote:
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What is the area of the region in which squares ABCD and EFGH overlap?

(1) EF bisects BC.

(2) The distance from point C to point E is \(2\sqrt{2}\) and the distance from point C to point F is \(2\sqrt{2}\).


Are You Up For the Challenge: 700 Level Questions

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What is the area of the region in which squares ABCD and EFGH overlap?  [#permalink]

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New post 08 Dec 2019, 18:54
Can't understand S2. Can someone please explain this?
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Re: What is the area of the region in which squares ABCD and EFGH overlap?  [#permalink]

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New post 12 Dec 2019, 05:41
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ShaliniShalini wrote:
Can't understand S2. Can someone please explain this?


ShaliniShalini

If we look at S2: it says distance of point C from point E and F is same and is equal to 2 root2

It means C is the center of the square EFGH. We are also given that side of square EFGH is 4

So, we can easily get the side of the small square asked; since we know the size of it now(which is 2)

Hope this helps!
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Re: What is the area of the region in which squares ABCD and EFGH overlap?   [#permalink] 12 Dec 2019, 05:41
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What is the area of the region in which squares ABCD and EFGH overlap?

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