Pac-Man in 2D

Geometry Level pending

A yellow character from a well-known video game franchise has a circular shape. By opening his mouth, he forms a circular sector with a radius of \(x\text{ cm}\).

If the arc corresponding to this sector also has a length of \(x\text{ cm}\), find the area of yellow region (the character's body).

Try solving Pac-Man in 3D!
This problem is original.
Image Credit: Prickätarpucken by Balthazar, Wikipedia.

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