Regular Polygon: Definition
A regular polygon is a flat shape where all sides are equal in length and all interior angles are equal in measure in Grade 6 math (Saxon Math, Course 1). An equilateral triangle (3 sides, 60° each), square (4 sides, 90° each), regular pentagon (5 sides, 108° each), and regular hexagon (6 sides, 120° each) are all regular polygons. The interior angle of a regular n-gon equals (n−2) × 180° ÷ n. Any polygon that fails either condition — unequal sides or unequal angles — is irregular. Recognizing regular polygons is essential for symmetry, tessellations, and circle inscriptions in geometry.
Key Concepts
Property If all the sides of a polygon have the exact same length and all the interior angles have the exact same measure, then the polygon is a regular polygon. All its sides are congruent (equilateral) and all its angles are congruent (equiangular).
Examples A square is a regular quadrilateral because all 4 sides are equal and all 4 angles are 90°. An equilateral triangle is a regular polygon because all 3 sides are equal and all 3 angles are 60°. A rectangle that is longer than it is wide is NOT regular because its sides are not all equal, even though its angles are all 90°.
Explanation A regular polygon is the super symmetrical celebrity of the shape world! Every single side is the exact same length, and every single angle is the exact same measure. It is perfectly balanced, with no lopsided parts. Think of a perfect square or a classic stop sign—no stretching or squishing allowed.
Common Questions
What is a regular polygon?
A polygon where all sides have the same length (equilateral) AND all interior angles have the same measure (equiangular).
Is a rectangle a regular polygon?
No. A rectangle has equal angles (90° each) but its sides are not all equal (unless it is also a square). A square IS a regular polygon.
What is the interior angle of a regular pentagon?
(5−2) × 180° ÷ 5 = 540° ÷ 5 = 108°.
What is the interior angle of a regular hexagon?
(6−2) × 180° ÷ 6 = 720° ÷ 6 = 120°.
What are examples of regular polygons?
Equilateral triangle (3), square (4), regular pentagon (5), regular hexagon (6), regular octagon (8).