structural:summarization
Convex sets and rectangles

Let C be a convex body in the plane (a convex set whose interior is non-empty). We can inscribe a rectangle r in C such that a homothetic copy R of r is circumscribed about C. The positive homothety ratio is at most 2 and: 1 2 ⋅ Area (R) ≤ Area (C) ≤ 2 ⋅ Area (r) {\displaystyle {\tfrac {1}{2}}\cdot \operatorname {Area} (R)\leq \operatorname {Area} (C)\leq 2\cdot \operatorname {Area} (r)}