1. Is this a variation of one of those box in a circle problems and is the answer 5.56cm^2?

Where you use Pythagoras and take 4^2 - 3^2 and you get 7^0.5 and solve that the area of the (imaginary) box is 28 then subtract from the circle with a 4 cm radius to get an area of 50.24 (3.14*4^2) then take the resulting figure of 22.24 and divide by 4?  Quote

2. If the area is 3.63cm.sq, you can try calculating the area of segment from area of sector minus area of triangle. For area of sector, u need the angle, which u can get thru Pythagoras principle.  Quote

3. You beat me to it @shafiq - I got the same result as you 3.628

https://www.mathopenref.com/segmentarea.html  Quote

4. Original Post Deleted
This will be stored in case something like it comes up in my kids' homework and I can then impress them with my intelligence!  Quote

5. Original Post Deleted
Side of square is 6 or 3?.
Area should be 3.6 either way?  Quote

6. Outer circle - Pi x 4 x 4 = 50.24
Inner Square - 6x6 = 36
Arc = (50.24-36)/4 = 3.56 = 3.6  Quote

7. I'm only here for the goat  Quote

8. A good idea to have a puzzle thread too   Quote

9. Original Post Deleted
Yeah that's what I was thinking of except for some reason I was thinking of a rectangle within a circle instead of a square so got the wrong inner area of the square which is 6*6.  Quote

10. Originally Posted by shri:
Outer circle - Pi x 4 x 4 = 50.24
Inner Square - 6x6 = 36
Arc = (50.24-36)/4 = 3.56 = 3.6
Wrong Shri

The area of the circle is OK.

The area of the square is wrong. You use Pythagoras theorem with a right angled triangle. Taking “c” as the radius and longest side, the unknown side ‘b’ is exactly half the base arc. The other side ‘a’ is the radius of the smaller circle. Therefore, half the arc base ‘b’ is the square root of ‘c’ squared minus ‘a’ squared, (4x4) - (3x3) = square root of 7. Funnily enough, 2xsquare root of 7 x 2xsquare root of 7 is 28, so the area of the square is 28.

Therefore area of circle - area of square = 50.265 - 28 = 22.265. The shaded area is 22.265/4 = 5.57 (to 2 decimal places)  Quote