For each n = 3, 4, 6 and 8, what are the areas of the circumscribed polygons with n sides?

Question

anonymous · Answer

$$A=1/2ap$$ is the formula I have to use.

anonymous · Answer

attachment

anonymous · Answer

@telliott99 please help

anonymous · Answer

Here.  Gimme a second

anonymous · Answer

Oh  sorry I don't run word

anonymous · Answer

it doesn't show any figures. it says to draw them yourself to help figure it out.

anonymous · Answer

For this exercise, consider a circle of radius 1, and corresponding circumscribed polygons with the number of sides n = 3, 4, 6, and 8.  Drawing a diagram will be extremely helpful.

A: For each n = 3, 4, 6 and 8, what are the areas of the circumscribed polygons with n sides?

anonymous · Answer

it said to use the formula i posted earlier.

anonymous · Answer

@telliott99 does it make any sense now

anonymous · Answer

So, we're supposed to draw a circle of radius 1, and then circumscribed polygon is one that just fits inside.  So starting with a triangle n=3, you are supposed to calculate the area.  And these are regular polygons, with all sides equal.  Right?

anonymous · Answer

|dw:1343936305561:dw|

anonymous · Answer

@smashinsam00

anonymous · Answer

Hope you come back, I love this problem.

anonymous · Answer

yes. sorry. my computer is super slow today. 
well at least I drew the first figure right. :)

anonymous · Answer

hold on i thought circumscribed polygon went around/on the outside of the circle

anonymous · Answer

and an inscribed polygon was when a polygon was inside the circle.
am i wrong?

anonymous · Answer

@telliott99

anonymous · Answer

I interpret that verb, circumscribed to mean the polygons are the objects of the action, maybe not

anonymous · Answer

But your formula looks like it works for the problem you describe, circles inside

anonymous · Answer

And it's easier

anonymous · Answer

|dw:1343937484093:dw|i checked my notes. it says that inscribed polygons are inside the circle, and circumscribed polygons are outside the circle.

anonymous · Answer

draw two altitudes of the triangle

anonymous · Answer

remember that it's equilateral

anonymous · Answer

i forgot to put the circle radius on the pic.

anonymous · Answer

If you do that you'll see that you can draw a right triangle with the radius as the shortest side, and half the base as the other side

anonymous · Answer

|dw:1343937774390:dw| like this