A square whose sides each measure ten centimeters can completely fit inside of a regular hexagon whose sides each measure ten centimeters?

Answer 1

Yes, a square with sides measuring ten centimeters can completely fit inside a regular hexagon with sides also measuring ten centimeters. The hexagon's interior angles and the distances from the center to the vertices allow for a square to be inscribed within it, as the square's diagonal is shorter than the hexagon's width at its widest points. Specifically, the diagonal of the square is approximately 14.14 centimeters, which is less than the distance between opposite sides of the hexagon. Thus, the square can be accommodated within the hexagon without any overlap.