# Area of inner and out square in circle

• May 2nd 2012, 04:16 PM
johnsy123
Area of inner and out square in circle
1) Considera circle with radius r. A square isinscribed in the circle and another is circumscribed around the circle.a) Calculatethe areas of the two squares.b) Usethese areas to approximate the area of the circle.

-Would the area of the inner square be r^2 and the area of the outter square be 4r^2?
• May 2nd 2012, 04:29 PM
skeeter
Re: Area of inner and out square in circle
Quote:

Originally Posted by johnsy123
1) Considera circle with radius r. A square isinscribed in the circle and another is circumscribed around the circle.a) Calculatethe areas of the two squares.b) Usethese areas to approximate the area of the circle.

-Would the area of the inner square be r^2 and the area of the outter square be 4r^2?

outer square expression is correct.

inner square ...

use the area formula for a rhombus ... $\displaystyle A = \frac{d^2}{2}$ , where $\displaystyle d$ is the diagonal length = circle's diameter

now substitute $\displaystyle 2r$ for $\displaystyle d$
• May 2nd 2012, 04:33 PM
johnsy123
Re: Area of inner and out square in circle
Why is it 2r?
• May 2nd 2012, 04:34 PM
johnsy123
Re: Area of inner and out square in circle
so it's r^2, as i said?
• May 2nd 2012, 04:35 PM
johnsy123
Re: Area of inner and out square in circle
So how would i use these areas to figure out the approximate area of the circle?
• May 2nd 2012, 04:36 PM
skeeter
Re: Area of inner and out square in circle
Quote:

Originally Posted by johnsy123
so it's r^2, as i said?

no ...

$\displaystyle \frac{(2r)^2}{2} = \frac{4r^2}{2} = 2r^2$
• May 2nd 2012, 04:58 PM
Soroban
Re: Area of inner and out square in circle
Hello, johnsy123!

Quote:

Consider a circle with radius $\displaystyle r$.
A square is inscribed in the circle and another is circumscribed around the circle.

a) Calculate the areas of the two squares.

b) Use these areas to approximate the area of the circle.

This diagram should illustrate the measurements.

Code:

    - *-------*-*-*-------*     : |  *    |    *  |     : | *-------+-------* | -     : |*| *    |r    * |*| :     : | |  *  |  *  | | :     : * |    * | * r  | * :_   2r * |      *      | *r√2     : * |    * | * r  | * :     : | |  *  |  *  | | :     : |*| *    |r    * |*| :     : | *-------+-------* | -     : |  *    |    *  |     - *-------*-*-*-------*