Thread: Area of inner and out square in circle

1. 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?

2. Re: Area of inner and out square in circle

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 ... $A = \frac{d^2}{2}$ , where $d$ is the diagonal length = circle's diameter

now substitute $2r$ for $d$

3. Re: Area of inner and out square in circle

Why is it 2r?

4. Re: Area of inner and out square in circle

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

5. 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?

6. Re: Area of inner and out square in circle

Originally Posted by johnsy123
so it's r^2, as i said?
no ...

$\frac{(2r)^2}{2} = \frac{4r^2}{2} = 2r^2$

7. Re: Area of inner and out square in circle

Hello, johnsy123!

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

,

,

area of inner circle in a square

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