Lesson: Polygons

I just added my solution here: http://gmatclub.com/forum/in-the-figure-shown-what-is-the-value-of-v-x-y...

Does that help?

You bet.

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

Cheers,
Brent

To be safe, I'd memorize the following:

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

Cheers,
Brent

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 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

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

Hi Philipp,

Which question are you referring to?

Cheers,
Brent

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

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

TRICKY!!!
Here's my full solution: https://gmatclub.com/forum/a-pentagon-with-5-sides-of-equal-length-and-5...

Tricky question!
Here's my full solution: https://gmatclub.com/forum/regular-polygon-x-has-r-sides-and-each-vertex...