Ellipse: 4x2+y2=1 with a=2, b=1. Area =πab=2π.
Curves y=∣x∣−1 and y=1−∣x∣ intersect at x=±1, forming a rhombus with vertices (0,1), (1,0), (0,−1), (−1,0).
Vertices (0,±1) lie on ellipse; (±1,0) are inside ellipse.
Area of rhombus =21×2×2=2.
Required area =2π−2=2(π−1).