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 500,000 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:

H,G,F and E are midpoints of the sides of square ABCD [#permalink]

Show Tags

11 Feb 2012, 00:48

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

72% (02:40) correct
28% (01:35) wrong based on 170 sessions

HideShow timer Statistics

H,G,F and E are midpoints of the sides of square ABCD. Arcs FG and EH are centered at B and D respectively, as shown above. If the side of the square ABCD is 4, what is the area of the shaded region HEFG?

A) 4(3-\(\pi\)) B) 2(4-\(\pi\)) C) 4(4-\(\pi\)) D) 2(6-\(\pi\)) E) 8(1+\(\pi\))

Re: H,G,F and E are midpoints of the sides of square ABCD [#permalink]

Show Tags

11 Feb 2012, 01:14

1

This post received KUDOS

Expert's post

nafishasan60 wrote:

H,G,F and E are midpoints of the sides of square ABCD. Arcs FG and EH are centered at B and D respectively, as shown above. If the side of the square ABCD is 4, what is the area of the shaded region HEFG?

A) 4(3-\(\pi\)) B) 2(4-\(\pi\)) C) 4(4-\(\pi\)) D) 2(6-\(\pi\)) E) 8(1+\(\pi\))

The legs of right isosceles triangles FAE and GCH equal to half of the side of the square, so to 4/2=2, hence their combined area is \(2*(\frac{1}{2}*2*2)=4\);

The same way the radii of arcs FG and EH equal to 4/2=2. Since both arcs are 90 degrees, then their commbined area is \(2*\frac{90}{360}*\pi*{r^2}=2\pi\);

The are of the square is 4^2=16, thus the area of the shaded region is \(16-(4+2\p)=2(6-\pi)\).

H,G,F and E are midpoints of the sides of square ABCD [#permalink]

Show Tags

26 Sep 2015, 05:52

I would ballpark for the right solution. Divide the square into 4 small squares (blue line) and call the midpoint M. From this you see that the shaded part within AFME and MGCH is always half. From this you have each 1/8 = 2/8 of the total square. Lastly also divide EMHD and FBGM further into halfes (red lines). There you see that the shaded region is half of 1/8 and therefore 1/16. So add 2/16 to 2/8 to get 3/8.

Attachment:

Unbenannt.png [ 7.56 KiB | Viewed 904 times ]

So we are looking for 3/8 of 16 = 6 in the answer choices. D is closest. _________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

gmatclubot

H,G,F and E are midpoints of the sides of square ABCD
[#permalink]
26 Sep 2015, 05:52

http://blog.ryandumlao.com/wp-content/uploads/2016/05/IMG_20130807_232118.jpg The GMAT is the biggest point of worry for most aspiring applicants, and with good reason. It’s another standardized test when most of us...

I recently returned from attending the London Business School Admits Weekend held last week. Let me just say upfront - for those who are planning to apply for the...