Polygon
A polygon is a closed two-dimensional figure formed by three or more straight line segments connected end-to-end. The segments are called sides, and the points where they meet are called vertices. Polygons are named by their number of sides: triangle (3), quadrilateral (4), pentagon (5), hexagon (6), heptagon (7), octagon (8). This Grade 7 math skill from Saxon Math, Course 2 establishes the basic vocabulary for all of plane geometry, enabling students to classify shapes, calculate perimeters and areas, and understand the properties of regular and irregular figures.
Key Concepts
Property When three or more line segments are connected to enclose a portion of a plane, a polygon is formed.
Examples A triangle is a polygon because it's a closed, 2D shape with 3 straight sides. A circle is not a polygon because its boundary is curved, not made of line segments. An open box is not a polygon because it is a 3D figure, not a plane figure.
Explanation Think of a polygon as a flat, closed shape made entirely of straight lines. It’s like building a fence where all the pieces are straight and they all connect to form a complete enclosure with no gaps. If your shape has any curves, isn't fully closed, or exists in 3D like a box, it's not a polygon!
Common Questions
What is a polygon?
A polygon is a closed plane figure made of three or more straight line segments. The segments are sides, and the corners where they meet are vertices. Examples include triangles, squares, and pentagons.
What are the names of polygons by number of sides?
Triangle (3 sides), quadrilateral (4), pentagon (5), hexagon (6), heptagon (7), octagon (8), nonagon (9), decagon (10). For larger numbers, the prefix is often combined with -gon.
Is a circle a polygon?
No. A polygon must have straight sides. A circle has no straight sides, so it is not a polygon.
What is the difference between a regular and an irregular polygon?
A regular polygon has all sides equal and all angles equal (like a square or equilateral triangle). An irregular polygon has sides or angles of different measures.
When do students learn about polygons?
Polygons are introduced in elementary school and studied with increasing rigor through Grade 7. Saxon Math, Course 2 covers polygon classification and properties throughout the geometry chapters.
What is the perimeter of a polygon?
The perimeter of any polygon is the sum of the lengths of all its sides. For a regular polygon, multiply the side length by the number of sides.
How do polygons connect to real-world shapes?
Stop signs (octagons), honeycomb cells (hexagons), floor tiles (squares, hexagons), yield signs (triangles) — polygons appear everywhere in architecture, nature, and design.