GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Feb 2019, 15:05

### GMAT Club Daily Prep

#### 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

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

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar

February 21, 2019

February 21, 2019

10:00 PM PST

11:00 PM PST

Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.
• ### Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT

# Figure ABCD (below) is a square with sides of length x. Arcs AB, AD

Author Message
TAGS:

### Hide Tags

Manager
Joined: 10 Mar 2014
Posts: 188
Figure ABCD (below) is a square with sides of length x. Arcs AB, AD  [#permalink]

### Show Tags

Updated on: 06 Feb 2019, 03:49
3
7
00:00

Difficulty:

75% (hard)

Question Stats:

52% (02:27) correct 48% (03:04) wrong based on 70 sessions

### HideShow timer Statistics

Figure ABCD (below) is a square with sides of length x. Arcs AB, AD, BC, and DC are all semicircles. What is the area of the red region, in terms of x?

Attachment:

semicircle.JPG [ 28.39 KiB | Viewed 13335 times ]

Originally posted by PathFinder007 on 02 Aug 2014, 07:30.
Last edited by Bunuel on 06 Feb 2019, 03:49, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Math Expert
Joined: 02 Sep 2009
Posts: 53063
Figure ABCD (below) is a square with sides of length x. Arcs AB, AD  [#permalink]

### Show Tags

02 Aug 2014, 14:39
5
12
PathFinder007 wrote:
Figure ABCD (below) is a square with sides of length x. Arcs AB, AD, BC, and DC are all semicircles. What is the area of the red region, in terms of x?

Not as hard as it seems. Consider the image below:

If we subtract the area of two blue semicircles, so the area of the whole circle, from the area of the square we get the combined area of two white regions, so the area of the four white regions we have in the original image, would be twice of that.

Now, since the length of the side of the square is x, then so is the diameter of the circle, which makes the radius equal to x/2 and the area of the circle (two blue semicircles) equal to $$\pi{r^2}=\frac{\pi{x^2}}{4}$$. The area of two white regions is therefore $$x^2 - \frac{\pi{x^2}}{4}$$ and the area of four white regions is $$2x^2 - \frac{\pi{x^2}}{2}$$.

The area of the red region equals to the area of the square minus the area of four white regions: $$x^2 - (2x^2 - \frac{\pi{x^2}}{2})= \frac{\pi{x^2}}{2} - x^2$$.

Attachment:

Untitled.png [ 6.34 KiB | Viewed 11084 times ]

_________________
##### General Discussion
Non-Human User
Joined: 09 Sep 2013
Posts: 9879
Re: Figure ABCD (below) is a square with sides of length x. Arcs AB, AD  [#permalink]

### Show Tags

06 Feb 2019, 03:50
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.
_________________
Re: Figure ABCD (below) is a square with sides of length x. Arcs AB, AD   [#permalink] 06 Feb 2019, 03:50
Display posts from previous: Sort by