How Many Sides

A polygon is defined by the number of straight edges it has. Each edge corresponds to one side, and the count of sides matches the count of vertices.

Common polygons by number of sides:

• 3 sides: triangle
• 4 sides: quadrilateral
• 5 sides: pentagon
• 6 sides: hexagon
• 7 sides: heptagon
• 8 sides: octagon
• 9 sides: nonagon
• 10 sides: decagon

Key formulas and notes:

• Sum of interior angles of an n-sided polygon: (n − 2) × 180 degrees
• Regular polygons have all sides and all interior angles equal; the measure of each interior angle in a regular n-sided polygon is [(n − 2) × 180] / n degrees.
• Convex polygons have all interior angles less than 180 degrees; concave polygons have at least one interior angle greater than 180 degrees.

Practical examples:

• A triangle: 3 sides, sum of interior angles = (3 − 2) × 180 = 180 degrees
• A square (a regular quadrilateral): 4 sides, each interior angle = 90 degrees
• A regular pentagon: 5 sides, each interior angle = [(5 − 2) × 180] / 5 = 108 degrees