Question Type 2: Finding the area of a closed region within a Voronoi Diagram Exercises

Given five points at $(0,0)$, $(1,1)$, $(-1,1)$, $(-1,-1)$ and $(1,-1)$, find the area of the Voronoi cell corresponding to $(0,0)$.

Six points lie at the vertices of a regular hexagon of circumradius $3$ centered at the origin. Find the area of the Voronoi cell of the center.

Five sites are at $(1,0)$, $(4,0)$, $(4,3)$, $(1,3)$ and the center site at $(2.5,1.5)$. Find the area of the Voronoi cell around $(2.5,1.5)$.

Eight points lie on a circle of radius $4$ equally spaced around the origin. Compute the area of the Voronoi cell of the origin.

Six points are at the vertices of a rectangle with corners $(0,0)$, $(6,0)$, $(6,4)$, $(0,4)$ and two additional points at midpoints of opposite edges: $(3,0)$ and $(3,4)$. The center site is at $(3,2)$. Compute the area of its Voronoi cell.

Ten points lie on a circle of radius $5$ equally spaced around the origin. Find the area of the Voronoi cell of the origin.

Four sites are at $(0,0)$, $(6,0)$, $(3,5)$, $(0,5)$ and the central site at $(2,2)$. Determine the area of the Voronoi cell of $(2,2)$.

Eight sites lie at $(2,2)$, $(-2,2)$, $(-2,-2)$, $(2,-2)$, $(3,0)$, $(0,3)$, $(-3,0)$, $(0,-3)$ with the center at $(0,0)$. Find the area of the Voronoi cell at the origin.

Twelve points lie equally spaced on a circle of radius $6$ around the origin. Compute the area of the Voronoi cell of the origin.

Six sites lie at $(2,1)$, $(5,1)$, $(4,4)$, $(1,3)$, $(0,1)$ and the center site at $(2,2)$. Determine the area of the Voronoi cell surrounding $(2,2)$.

Seven sites are at $(1,1)$, $(5,2)$, $(3,6)$, $(0,4)$, $(-1,1)$, $(3,0)$ and the central site at $(2,2)$. Compute the area of the Voronoi cell around $(2,2)$.