Let the area enclosed by the movement route A and the X axis be S 1, and every 90° S2 and S3.
1, A-A 1, locus of point a: 1/4 circle, R 1= 1,
S 1=S semicircle aa 1b = π r 1 2/4 = π/4.
2. A 1-A2, the locus of point A: 1/4 circle, R2=√2.
S2=S semicircle A 1A2C+S squared ABCD = π R2 2/4 = π/2+ 1.
3, A2-A3, the locus of point A: 1/4 circle, R3= 1,
S3=S semicircle = π R3 2/4 = π/4
Conclusion: S total =S 1+S2+S3=π+ 1.