Review question

# Can we find a formula for an island's territorial waters? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R5534

## Question

An island is in the shape of a convex polygon with perimeter $p$ miles. Its territorial water consists of all points of the sea within $r$ miles of its coast. Assuming that no other land is within $r$ miles of the island and that the earth is flat, prove that the area of the territorial water is $(pr+\pi r^2)$ square miles.

Consider whether the same formula would hold

1. if the island were convex but not polygonal,

2. if it were polygonal but not convex.