Lesson: Polygons

Comment on Polygons

Hi, Can someone explain the solution for the first 650/800 exercise(the pentagram)? My mind refuse absolutly to understand the explanations on the comment section.
Cheers,
Ben
gmat-admin's picture

Yes, it's much easier that way ! Thank you Brent !

Hi, could you please help explain the solution to the following question:

https://gmatclub.com/forum/in-the-figure-shown-what-is-the-value-of-v-x-y-z-w-134894.html

Thanks!
gmat-admin's picture

Do we have to know the names of polygons? ex. hexangon?
gmat-admin's picture

To be safe, I'd memorize the following:

5 sides: pentagon
6 sides: hexagon
8 sides: octagon

Cheers,
Brent

Hi Brent, please help me with a solution to the below question.

https://gmatclub.com/forum/in-the-figure-shown-what-is-the-value-of-v-x-y-z-w-134894.html
gmat-admin's picture

Hi Jalaj,

Here's my step-by-step solution: https://gmatclub.com/forum/in-the-figure-shown-what-is-the-value-of-v-x-...

Cheers,
Brent

Hi Brent,

Failing to get an answer for this one:

A rectangular box is inches high, inches wide, and 5 inches deep. What is the greatest possible straight-line distance, in inches, between any two points on the box?

A 10
B 12
C 13
D 6* Sq root of 2 + 5
E 12* Sq root of 2 + 5



gmat-admin's picture

Hi Jalaj,

Looks like some numbers (dimensions) are missing from your question.
That said, I have a VERY similar question here: https://www.gmatprepnow.com/module/gmat-geometry/video/869

Check out the solution to that video question and see if you can apply it to your question.
NOTE: In the video https://www.gmatprepnow.com/module/gmat-geometry/video/869, I solve the question in 2 different ways.
At 2:32 in the video, I introduce a nifty formula for solving these kinds of questions.

Cheers,
Brent

Got it! I wonder how I missed this lesson! Thanks very much.

https://gmatclub.com/forum/in-the-figure-above-polygon-n-has-been-partially-covered-by-a-piece-261041.html

Hello Mr.
I'm little confused with your solution here,
you said that statement 1 is sufficient and statement 2 is not! how come the answer is both together sufficient.
I learnt,if i'm right, from DS strategy that If statement 1 alone sufficient and statement 2 is not, then it can't be true the answer is together!
could you please clear my confusion.
Thanks your videos help my score a lot
gmat-admin's picture

Good catch.
I should have said that statement 1 is NOT sufficient.
I've edited my answer.
Thanks!

Hey Brent,

is there a minimal value for the lengths of Polygons?

Like in this Q:

It i max. 14 and >0 I guess?

Cheers,

Philipp
gmat-admin's picture

Hi Philipp,

Which question are you referring to?

Cheers,
Brent

I am sorry, here it is:

https://gmatclub.com/forum/in-pentagon-pqrst-pq-3-qr-2-rs-4-and-st-5-which-168634.html

gmat-admin's picture

Link: https://gmatclub.com/forum/in-pentagon-pqrst-pq-3-qr-2-rs-4-and-st-5-whi...

There's a nice rule for the missing side of a TRIANGLE.
If we know a triangle has sides of length A and B, then we can say;
(difference between A and B) < 3rd side < (sum of A and B)

There's no convenient rule for polygons with more than 3 sides.
That said, we CAN say:
(length of missing side) < (sum of the other sides)

For that particular question (liked above), the nature of the given sides allow us to say:
0 < (length of missing side) < 14

However, if the 4 given sides had length 10, 2, 1 and 1, then we'd say:
6 < (length of missing side) < 14

Cheers,
Brent

Hey Brent,

regarding this Q:

https://gmatclub.com/forum/a-pentagon-with-5-sides-of-equal-length-and-5-interior-angles-of-equal-294336.html

How can we in the first statement, knowing the radius, figure out the length of the side of the polygon? Is that actually possible?

Cheers,

Philipp
gmat-admin's picture

Question link: https://gmatclub.com/forum/a-pentagon-with-5-sides-of-equal-length-and-5...

Yes, it's possible to determine the length of the sides, but we'd need to use some trigonometry.

The important thing is that statement 1 "locks in" the size of the pentagon (for more on this see: https://www.gmatprepnow.com/module/gmat-geometry/video/884)

Keep in mind that we're dealing with a regular pentagon.
There are infinitely many regular pentagons, each with its own unique area.
Also, for each unique pentagon, there is one unique circle that the pentagon can be inscribed in.
So, once we know the area of the circle is 16π square centimeters, we know that there is exactly one unique regular pentagon that can be inscribed in this unique circle.

So, statement 1 is sufficient.

Does that help?

Cheers,
Brent

Yes Brent, thanks for the explanation!

Philipp

Add a comment

Brag up your Geometry Mastery

Now that you’ve mastered GMAT Geometry, it’s time to let the world know!

Change Playback Speed

You have the option of watching the videos at various speeds (25% faster, 50% faster, etc). To change the playback speed, click the settings icon on the right side of the video status bar.

Have a question about this video?

Post your question in the Comment section below, and I’ll answer it as fast as humanly possible.

Free “Question of the Day” emails!