Regular polygon
A regular polygon is a polygon with all sides equal in length and all interior angles equal in measure. The perimeter of a regular polygon is calculated using P = n times s, where n is the number of sides and s is the side length. A regular hexagon with 6 sides of 8 mm each has a perimeter of 48 mm. This Grade 7 math skill from Saxon Math, Course 2 establishes the vocabulary and properties of regular polygons — including triangles, squares, pentagons, hexagons, and octagons — which are foundational for geometry, tessellations, and trigonometry.
Key Concepts
Property The sides of a regular polygon are equal in length. To find its perimeter, multiply the number of sides ($n$) by the length of one side ($s$): $P = n \times s$.
Examples A regular hexagon (6 sides) with each side measuring 8 mm has a perimeter of $6 \times 8 \text{ mm} = 48 \text{ mm}$. A regular octagon (8 sides) with each side measuring 12 inches has a perimeter of $8 \times 12 \text{ inches} = 96 \text{ inches}$.
Explanation Why add the same number over and over again? For regular polygons, where all sides are identical twins, use this awesome shortcut! Just multiply the number of sides by the length of one side to get the perimeter instantly.
Common Questions
What is a regular polygon?
A regular polygon has all sides the same length and all interior angles equal. Examples include equilateral triangles, squares, regular pentagons, hexagons, and octagons.
How do I find the perimeter of a regular polygon?
Multiply the number of sides by the length of one side: P = n times s. A regular octagon with sides of 12 inches has a perimeter of 8 times 12 = 96 inches.
What are common regular polygons students should know?
Key regular polygons: equilateral triangle (3 sides), square (4 sides), regular pentagon (5 sides), regular hexagon (6 sides), regular heptagon (7 sides), regular octagon (8 sides), regular decagon (10 sides).
What is the sum of interior angles of a regular polygon?
The sum of interior angles = (n - 2) times 180 degrees, where n is the number of sides. For a regular hexagon: (6 - 2) times 180 = 720 degrees. Each angle is 720 divided by 6 = 120 degrees.
When do students learn about regular polygons?
Regular polygons are introduced in Grade 4-5 and studied in depth in Grade 7. Saxon Math, Course 2 covers them in Chapter 7 as part of polygon properties.
What makes a polygon irregular?
A polygon is irregular if its sides are not all equal in length or its angles are not all equal. A rectangle has equal angles but unequal sides (unless it is a square), so it is irregular.
How are regular polygons used in real life?
Regular hexagons tile a plane perfectly (like honeycomb), regular pentagons and hexagons form a soccer ball, and octagonal shapes are used in stop signs. Understanding regular polygons connects math to design and nature.