Thread: 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?

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 ... , where is the diagonal length = circle's diameter

now substitute for

Why is it 2r?

so it's r^2, as i said?

So how would i use these areas to figure out the approximate area of the circle?

Originally Posted by johnsy123

so it's r^2, as i said?

no ...

Hello, johnsy123!

Consider a circle with radius .
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    * |*| :
    : | *-------+-------* | -
    : |   *     |     *   |
    - *-------*-*-*-------*