Math people out there: How would you solve this problem.

[TheFriendlyAnarchist]

Okay, this was an extra credit assignment that my teacher gave out. I worked on it for a while (ALG 2 btw) and got a couple pages of notes, before finally getting it right.

I want to see how y'all would have progressed and done the problem.

You have a circle with a radius of 1. Inscribed within this circle is an octagon, each of the vertices's touching the edge of the circle. Determine the area between the vertices's and the circle (Or find the area of the circle and take from that the area of the octagon).

[flvegan]

1. I'd have cheated off the smart girl directly to my left.

[TheFriendlyAnarchist]

10. It would have been 'cute' more than smart though

There aren't any other girls around me, so smart wouldn't have been an option.

[Dr. Strange]

2. I would have focused on the first quadrant.

Set up a quarter circle centered at the origin, draw three vertices: (1,0), (sqrt(2)/2,sqrt(2)/2), and (0,1). Then use those to make two triangles which form a quarter of the octagon.

Which means I get pi - 2sqrt(2).

[TheFriendlyAnarchist]

5. Well played, and that's the right answer.

I made a square in the center, found the sides, and then made four kites out of the octagon.

[Dr. Strange]

11. Woohoo!

And geometry's my weakest subject! (Mathematically speaking.)

[Pierre.Suave]

3. Simple

Find the area of the circle and the octagon, subtract octagon area from circle area and get an answer.

Octagon area: http://mathcentral.uregina.ca/QQ/database/QQ.09.01/laurie2.html

Edit: Area of the circle is 3.14 A=(pi)R^2

edit, answer coming soon, I just figured out how to get it, draw straight lines from the vertices to the midpoint, you will form triangles with two sides equal to 1, get area, add up, and then subtract.

[Pierre.Suave]

4. I got it

want to know how?

[TheFriendlyAnarchist]

7. I finished it and turned it in, I was curious how DU would do it though.

Answer is pi-2*sqrt2 correct?

[TheFriendlyAnarchist]

6. Yea, but where's the fun in simple?

yea, but you can't determine the base or the height of those wonderful isosceles triangles with the information given.

[hvn_nbr_2]

8. Extra extra credit question

The problem, as stated, doesn't say if the octagon is regular/equilateral (all sides the same length)(I'm not sure which is the proper word). Does it matter or is the answer the same for any octagon?

[TheFriendlyAnarchist]

9. That was my mistake. Yes, it is regular.

However, as long as they had the same area, it wouldn't matter. Finding that area is a whole 'nother concern if it is irregular.

[Dr. Strange]

12. It's definitely a regular octagon...

I saw a box of Bran Flakes next to it!
:)

[carly denise pt deux]

13. let me get out my protractor, compass, slide ruler

the hypotenuse is connected to the pi, the pi is connected to the right angle, the right angle is connected to the Isosceles........oh, I used the math tools as drum sticks while I sang my ditty....I have no idea what the answer is, I would have to ask my kid, who would probably know the answer. I stopped helping her with her math in the 3rd grade.
Carly

[pokerfan]

14. It's a simple SAS trig problem

There are 8 indentical isosceles triangles. We know the interior angle and the length of the two sides. Compute the area of the triangle, multiply by 8 and you have the area of the octogon.

[Rabrrrrrr]

15. Simple - find area of circle and subtract area of octagon.

Not very difficult, since the octagon is a regular one.