[Elementary/Middle School Math] Please help with this geometry problem

This is the way I did it not sure if correct as i’m using my phone’s notepad and calculator but might help? I’ll probably just get downvoted more but here goes..

If the area of the square is 100cm and the area of the circle is 78.57, if we subtract the circle from the square we get the outsides area spaces as 21.43. Divide this by two to get the outside the circle areas on either side of the circle 10.715. If we can assume the big arcs are essentially two quarter circles of 10cm radius, then we can double the original circle area to get 157.14 as the area of the whole big circle one of those quarters represents. If we divide this by four we get the size of each quarter circle at 39.35. If we subtract the outside the circle on one end from the big quarter circle, we get the shaded region on one side of 28.63. Double this is the area of both, 57.27.. I think.

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