# Lesson: Polygons

## Comment on Polygons

### Hi, Can someone explain the

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 ### Hi Brent, how did you deduce

Hi Brent, how did you deduce that the pentagon in the centre is a regular pentagon? ### In my solution (https:/

In my solution (https://gmatclub.com/forum/in-the-figure-shown-what-is-the-value-of-v-x-...), I worked with a "perfect" star in which all of the angles (at each point) are the same.
Since all of the angles are the same, the resulting pentagon in the center must be a regular pentagon.

I hope that helps.

Cheers, Brent

### Yes, it's much easier that

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

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

Thanks! ### Do we have to know the names

Do we have to know the names of polygons? ex. hexangon? ### To be safe, I'd memorize the

To be safe, I'd memorize the following:

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

Cheers,
Brent

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

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,

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 ### Hi Jalaj,

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

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

### https://gmatclub.com/forum/in

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 ### Good catch.

Good catch.
I should have said that statement 1 is NOT sufficient.
Thanks!

### Hey Brent,

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 ### Hi Philipp,

Hi Philipp,

Which question are you referring to?

Cheers,
Brent

### I am sorry, here it is:

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 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,

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 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

Yes Brent, thanks for the explanation!

Philipp

### Hi Brent,

Hi Brent,

Can you help on this question please ?

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

Thanks,
Karaan ### Hi Brent,

Hi Brent,

Could you please solve this question?

Regular polygon X has r sides, and each vertex has an angle measure of s, an integer. If regular polygon Q has r/4 sides, what is the greatest possible value of t, the angle measure of each vertex of Polygon Q?

A. 2
B. 160
C. 176
D. 178
E. 179

I got choice D, as the max can be 178 and the other two angles 1 each (considering that Polygon X has 12 sides, then polygon X would have 3 sides, which makes the sum of all angles 180).

Thanks 