Question

a polygon is broken up into 4 non-overlapping triangles by drawing lines from one vertex to all other non-adjacent vertices. what is the name of the polygon?

octagon
hexagon
heptagon
quadrilateral

Explanation:

Relate number of triangles to number of sides

An \(n\)-sided polygon can be partitioned into \(n - 2\) non-overlapping triangles by drawing diagonals from a single vertex to all other non-adjacent vertices.

Solve for the number of sides

Set the number of triangles equal to 4:

$$ n - 2 = 4 $$

$$ n = 6 $$

Identify the polygon name

A polygon with 6 sides is called a hexagon.

Answer:

• octagon
• hexagon (Correct answer)
• heptagon
• quadrilateral