The circle has radius of 5 cm.
the square of ABC is placed inside the circle and part of it shaded.
lets find the area of shaded region

2. Originally Posted by janeyandtaz
The circle has radius of 5 cm.
the square of ABC is placed inside the circle and part of it shaded.
lets find the area of shaded region
The diagonal of the big square is 10cm because that's the diameter of the circle.

So the big square has side length $\frac {10}{\sqrt 2} = 5 \sqrt 2$.

That's the same length as the diagonal of the small square. So you can work out the side length of the small square, and so square that to get its area.

3. Hello, janeyandtaz!

The circle has radius of 5 cm.
The square ABCD is placed inside the circle and part of it shaded.
Find the area of shaded region.
Code:
              * * *
*      P    *
A o - - - o - - - o B
*|     *:::*     |*
|   *:::::::*   |
*  | *:::::::::::* |  *
*  *:::::::::::::::oQ *
*  | *:::::::::::* |  *
|   *:::::::*   |
*|     *:::*     |*
D o - - - * - - - o C
*           *
* * *

The diagonal of the large square $AC$ equals the diameter: 10 cm.

In triangle $ABC,\;PQ$ joins the midpoints of two sides.
Hence, it is half the length of the third side $AC.$

So the side of the small square $PQ$ is 5 cm.

Therefore, the area of the small square is: . $5^2 \,=\,25\text{ cm}^2$

4. Hi yaa...

Soroban, u got it exactly

5. Originally Posted by janeyandtaz
Hi yaaaa...
Soroban, u got it rite!
D'oh! didn't I, then?