9. Sliding Stick II
Setup
A stick of length 1 stands upright against a wall.
The bottom slides outward; the top slides down.
Rules
- The stick maintains contact with both wall and ground
- Motion ends when the stick lies flat
Question
What is the total area swept by the stick?
Answer format
Enter a number rounded to 2 decimal places.
Your Answer
Need help?
Hint 1
Think about what region the stick DOESN'T sweep. Is there a curve the stick always stays tangent to?
Hint 2
Consider a quarter circle centered at the corner (1,1) with radius 1. Check if the stick remains tangent to this curve.
Hint 3
What is the area of a quarter circle with radius 1?