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

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Math Expert
Joined: 02 Sep 2009
Posts: 60468
What is the area of the region in which squares ABCD and EFGH overlap?  [#permalink]

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04 Dec 2019, 02:42
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Difficulty:

55% (hard)

Question Stats:

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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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:

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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Joined: 05 Aug 2019
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What is the area of the region in which squares ABCD and EFGH overlap?  [#permalink]

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08 Dec 2019, 18:54
Can't understand S2. Can someone please explain this?
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Joined: 13 Apr 2019
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Schools: Kellogg '22
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Re: What is the area of the region in which squares ABCD and EFGH overlap?  [#permalink]

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12 Dec 2019, 05:41
1
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!
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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