Circumscribed circle - inscribed circle area formula

In summary, the formula for finding the area of a circle is A = πr^2, where r is the radius of the circle. The area of a circumscribed circle is always larger than the area of an inscribed circle and is exactly twice the area. To find the radius of a circumscribed circle using the area formula, you can rearrange the formula to solve for r, which would be r = √(A/π). The circumscribed circle and inscribed circle can exist in any shape with a circular boundary, as long as the radius is known.
  • #1
guss
248
0
I'm looking for a formula that subtracts the area of an inscribed circle of a shape from the circumscribed area of the shape. I've confused myself on this one and can't seem to figure it out.

The shape is a regular polygon (all sides and angles are equal). What should be given to "plug in" is each side is of length L and there are s sides.

Can anyone help me? Thanks!
 
Mathematics news on Phys.org
  • #2
Got it![tex]\frac{L^{2} \pi\ }{4}[/tex]

Where [tex]L[/tex] is the length of each side. Works for any regular polygon.Sorry, you can close this thread if you please.
 

What is the formula for finding the area of a circumscribed circle?

The formula for finding the area of a circumscribed circle is A = πr2, where r is the radius of the circle.

What is the formula for finding the area of an inscribed circle?

The formula for finding the area of an inscribed circle is A = πr2, where r is the radius of the circle.

What is the relationship between the area of a circumscribed circle and the area of an inscribed circle?

The area of a circumscribed circle is always larger than the area of an inscribed circle. In fact, the area of the circumscribed circle is always exactly twice the area of the inscribed circle.

How do you find the radius of a circumscribed circle using the area formula?

To find the radius of a circumscribed circle using the area formula, you can rearrange the formula to solve for r. It would be: r = √(A/π).

Can the circumscribed circle and inscribed circle exist in any shape other than a perfect circle?

Yes, the circumscribed circle and inscribed circle can exist in any shape, as long as the shape has a circular boundary. The formula for finding the area will still be the same, as long as the radius of the circle is known.

Similar threads

Replies
9
Views
729
Replies
6
Views
757
Replies
10
Views
1K
Replies
7
Views
2K
Replies
7
Views
5K
  • General Math
Replies
4
Views
4K
Replies
2
Views
997
  • General Math
Replies
1
Views
1K
Replies
1
Views
3K
Replies
1
Views
1K
Back
Top