SideOne of the straight line segments that make up the polygon.
VertexA corner, where two sides meet. More than one: vertices.
Interior angleThe angle inside the polygon between two sides.
Exterior angleBetween one side and the next side extended outward.
DiagonalJoins two vertices that are not next to each other.
CenterThe point the same distance from every vertex.
RadiusFrom the center to a vertex.
ApothemFrom the center to the middle of a side, at right angles.
Reflex angleAn interior angle over 180°: it makes the polygon concave.
How this list was compiled: All read 2026-09-23 for facts only; nothing copied. (1) OpenStax, Contemporary Mathematics, 10.4 Polygons, Perimeter, and Circumference, https://openstax.org/books/contemporary-mathematics/pages/10-4-polygons-perimeter-and-circumference: sides and vertices; regular polygons (all sides and angles equal); interior angles; an exterior angle is formed by extending a side beyond the figure; a polygon is concave when an interior angle is greater than 180°. (2) OpenStax, Contemporary Mathematics, 10.6 Area, https://openstax.org/books/contemporary-mathematics/pages/10-6-area: the apothem of a regular polygon starts at the center and is perpendicular to a side; the radius starts at the center and extends to a vertex; a diagonal runs from one vertex to the opposite vertex. (3) Wikipedia, Polygon, https://en.wikipedia.org/wiki/Polygon: sides (edges) and vertices (corners); a concave polygon has at least one interior angle greater than 180°. (4) Wikipedia, Internal and external angles, https://en.wikipedia.org/wiki/Internal_and_external_angles: an interior angle is formed by two adjacent sides; an exterior angle by one side and a line extended from an adjacent side. (5) Wikipedia, Diagonal, https://en.wikipedia.org/wiki/Diagonal: a segment joining two vertices not on the same edge. (6) Wikipedia, Apothem, https://en.wikipedia.org/wiki/Apothem: from the center to the midpoint of a side, perpendicular to it. (7) Wikipedia, Angle, https://en.wikipedia.org/wiki/Angle: a reflex angle is between 180° and 360°. Licence: own work
The drawing: Drawn for this site by script, 2026-09-23. Licence: own work
How it works
The parts of a polygon are its sides, vertices and angles, plus the diagonals inside it. A regular polygon adds a center, a radius and an apothem, and a concave polygon has a reflex angle.
Read the full guide
Three shapes, nine parts
The pentagon shows the parts every polygon has. The regular hexagon adds the ones that need a center, and the dart shows the reflex angle that makes a polygon concave. Quiz me asks all nine.
Radius or apothem?
Both start at the center. The radius runs to a vertex. The apothem runs to the middle of a side and meets it at a right angle, so it is the shorter of the two.
At any vertex of a convex polygon, the interior and exterior angles add up to 180°.
Questions and answers
What are the parts of a polygon?
Sides, vertices and angles. Each side is a straight segment, and each vertex is a corner where two sides meet. Inside are interior angles and diagonals; outside, exterior angles. A regular polygon also has a center, a radius and an apothem.
What is the apothem of a polygon?
The segment from the center of a regular polygon to the middle of a side, at a right angle to it. It gives the area: half the apothem times the perimeter.
How many diagonals does a polygon have?
n(n − 3) ÷ 2 for n sides: every vertex joins all the others except itself and its two neighbors, and each diagonal is counted from both ends. A pentagon has 5 and a hexagon 9.