The math of all regular polygons inscribed within a unit circle.

Within a unit circle, the area of any inscribed regular polygon = sides * cos(180/sides) * sin(180/sides). units^2.
Within a unit circle, the perimeter of any inscribed regular polygon = 2 * sides * sin(180/sides). units.

Now, I wonder: what questions does this stimulate?

Impressed? I know, I am! :)

Is it Klingon?

Will this be on the test?

@HiramHolliday said in #2:

Is it Klingon?

The source of this isn't Klingon. And, I'm not familiar with Klingons; I am familiar with Polygons though! Why do you ask?

@Frogster64 said in #3:

Will this be on the test?

I currently don't know of any test this will be on, but in any event, knowing these formulas should help for it, just in case. :)

Is a polygon a dead parrot?

@Approximation said in #1:

Within a unit circle, the area of any inscribed regular polygon = sides * cos(180/sides) * sin(180/sides). units^2.
Within a unit circle, the perimeter of any inscribed regular polygon = 2 * sides * sin(180/sides). units.

bro u r talking in an undiscovered language

I don't think proving this is hard, considering that a regular polygon can be divided into triangles of equal area; like how a pizza slice is cut.

Infact, if the circle is of any radius, you just multiply the above area you found by the square of the circle's radius.

@Passionate_Player said in #8:

Infact, if the circle is of any radius, you just multiply the above area you found by the square of the circle's radius.

Scaling a unit circle by a factor of r, I believe should increase/decrease the area by a factor of r^2. Likewise, the proportions of an inscribed square should increase similarly, being the same percentage of area in a unit circle as a circle with a scaled radius.