Math: Polygons

excellent ! - thank you +1

Thanks Bunuel for such comprehensive notes....

Hi Bunuel,
Nice post can you extend this by including solid figures also.

math-3-d-geometries-102044.html

One more masterpiece from Bunuel...... Kudos...!!

The below is the concept used to derive the above formula for Number of diagonals .

As we know, to make a diagonal (a line), we need 2 (a pair of) points.
if i have n sided plygon, i need to select different par of points.

This can be doen in \(nc2\) ways
but thease pairs include all the sides also. hence subtract the number of sides (\(n\)), whiich are not diagonals, from the above
==> \(The Number of diagonals\) is
==> \(nc2-n\)
==> \(\frac{n(n-1)}{2} - n\)
==> \(\frac{(n^2-3n)}{2}\)
==> \(\frac{n(n-3)}{2}\)

Regards,
Murali.

Kudos?

Great post !!! THANK YOU
+ Kudo

Hi, Super awesome post by the genius again.

One small doubt. if a DS question talks about a parallelogram and then goes on to say that the diagonals are equal. Does it imply we have a rectangle ?

Further the post says that should the diagonals of a parallelogram be equal and the angles be bisected by it, its a square. But I think this will happen in case of both a rect and a square ?

Hi, Super awesome post by the genius again.

One small doubt. if a DS question talks about a parallelogram and then goes on to say that the diagonals are equal. Does it imply we have a rectangle ?

Further the post says that should the diagonals of a parallelogram be equal and the angles be bisected by it, its a square. But I think this will happen in case of both a rect and a square ?

many thanks for this !

Great post....Thanks

great post..thanks Bunuel

another awesome post... thanks Benuel

Many thanks!! could find the info only there!! highly appreciate

Amazing post, thank you!

Bunuel, thanks once again for your great work.

Although this has already been asked in some form on this thread, I would like to ask you to add a set of sufficient properties that would allow a GMAT taker to determine the type of a quad. I find that this aspect is very moot in the Manhattan Geometry guide. The set of properties should be as minimal as possible in order to be useful on DS questions. For example (please correct me if those properties are not true),

Parallelogram
Given a quad, if its opposite sides are parallel then it is a parallelogram.
Given a quad, it its opposite sides are equal then it is a parallelogram.

Rhombus
Given a quad, if its diagonals are perpendicular bisectors then it is a rhombus.

Square
Given a quad, if its sides are equal then it is a square.
Given a quad, if its angles are equal (90 degrees) then it is a square.
Given a quad, if its diagonals are equal then it is a square.

Thanks in advance.

Regular polygon's area can be calculated,other polygon's area can also be calculated using graph coordinates,but i have heard that polygon's area can be calculated using sides and external angles is it true?if it is what is the method?