Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

In the figure above, square AFGE is inside square ABCD such [#permalink]
10 Feb 2012, 05:39

2

This post received KUDOS

3

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

57% (03:14) correct
43% (01:54) wrong based on 58 sessions

In the figure above, square AFGE is inside square ABCD such that G is on arc BD, which is centered at C. If DC=8, what is the area of square AFGE (area of square of side s = s^2)?

A) 32 (1-\sqrt{2}) B) 32 (3-2\sqrt{2}) C) 64 (\sqrt{2} - 1)^2 D) 64 - 16\pi E) 32 - 4\pi

Re: area of square [#permalink]
10 Feb 2012, 06:01

1

This post received KUDOS

nafishasan60 wrote:

In the figure above, square AFGE is inside square ABCD such that G is on arc BD, which is centered at C. If DC=8, what is the area of square AFGE (area of square of side s = )?

A) 32 (1-) B) 32 (3-2) C) 64 ( - 1) D) 64 - 16 E) 32 - 4

we can find diagonal AC = 8 \sqrt{2} so AG = AC -CG( radius of the arc) = 8\sqrt{2} - 8 now AE = AG/\sqrt{2} = 8\sqrt{2} - 8 / \sqrt{2} IMO B.. _________________

Fire the final bullet only when you are constantly hitting the Bull's eye, till then KEEP PRACTICING.

Re: area of square [#permalink]
10 Feb 2012, 06:41

Took me 10 mins... but I got it... Surprising it wasn't super difficult. Since C is the center of the Circle, the length of GC = 8. Since AEFG touches the circle with it's corner, we know the angle of GC is 45%. When you spilt a square in half diagonally it's going to be 45 degrees. If the angle GC is 45% you know the triangle form with would be a 1:1:root(2). Since GC is the hypotenuse the other 2 will be 8/root(2). The length of FG = 10 (height of the square) - 8/root(2) (height of the triangle). [10-8/root(2)]^2 = 32 (3-2*root(2)).

Answer is B. Hard to explain without a graph and too lazy to make one. Sorry

In the figure above, square AFGE is inside square ABCD such [#permalink]
10 Feb 2012, 08:00

Expert's post

nafishasan60 wrote:

In the figure above, square AFGE is inside square ABCD such that G is on arc BD, which is centered at C. If DC=8, what is the area of square AFGE (area of square of side s = s^2)?

A) 32 (1-\sqrt{2}) B) 32 (3-2\sqrt{2}) C) 64 (\sqrt{2} - 1)^2 D) 64 - 16\pi E) 32 - 4\pi

No additional drawing is needed.

The length of the diagonal AG is AC-GC;

AC is a diagonal of a square with a side of 8, hence it equal to 8\sqrt{2} (hypotenuse of 45-45-90 triangle);

GC=DC=radius=side=8;

Hence AG=8\sqrt{2}-8=8(\sqrt{2}-1);

Area of a square: \frac{diagonal^2}{2}=\frac{(8(\sqrt{2}-1))^2}{2}=32*(\sqrt{2}-1)^2=32*(3-2\sqrt{2}).

Re: In the figure above, square AFGE is inside square ABCD such [#permalink]
15 Jul 2014, 13:13

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

In the figure above, square AFGE is inside square ABCD such [#permalink]
20 Aug 2014, 14:09

Bunuel wrote:

nafishasan60 wrote:

In the figure above, square AFGE is inside square ABCD such that G is on arc BD, which is centered at C. If DC=8, what is the area of square AFGE (area of square of side s = s^2)?

A) 32 (1-\sqrt{2}) B) 32 (3-2\sqrt{2}) C) 64 (\sqrt{2} - 1)^2 D) 64 - 16\pi E) 32 - 4\pi

No additional drawing is needed.

The length of the diagonal AG is AC- AG;

AC is a diagonal of a square with a side of 8, hence it equal to 8\sqrt{2} (hypotenuse of 45-45-90 triangle);

AG=DC=radius=side=8;

Hence AG=8\sqrt{2}-8=8(\sqrt{2}-1);

Area of a square: \frac{diagonal^2}{2}=\frac{(8(\sqrt{2}-1))^2}{2}=32*(\sqrt{2}-1)^2=32*(3-2\sqrt{2}).

Answer: B.

Bunuel , I think you meant GC in place of AG in the highlighted portion.

Re: In the figure above, square AFGE is inside square ABCD such [#permalink]
21 Aug 2014, 03:09

Expert's post

maggie27 wrote:

Bunuel wrote:

nafishasan60 wrote:

In the figure above, square AFGE is inside square ABCD such that G is on arc BD, which is centered at C. If DC=8, what is the area of square AFGE (area of square of side s = s^2)?

A) 32 (1-\sqrt{2}) B) 32 (3-2\sqrt{2}) C) 64 (\sqrt{2} - 1)^2 D) 64 - 16\pi E) 32 - 4\pi

No additional drawing is needed.

The length of the diagonal AG is AC- AG;

AC is a diagonal of a square with a side of 8, hence it equal to 8\sqrt{2} (hypotenuse of 45-45-90 triangle);

AG=DC=radius=side=8;

Hence AG=8\sqrt{2}-8=8(\sqrt{2}-1);

Area of a square: \frac{diagonal^2}{2}=\frac{(8(\sqrt{2}-1))^2}{2}=32*(\sqrt{2}-1)^2=32*(3-2\sqrt{2}).

Answer: B.

Bunuel , I think you meant GC in place of AG in the highlighted portion.

For my Cambridge essay I have to write down by short and long term career objectives as a part of the personal statement. Easy enough I said, done it...