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Regular Heptagon — Definition, Formula & Examples

A regular heptagon is a seven-sided polygon where every side has the same length and every interior angle has the same measure.

A regular heptagon is an equilateral and equiangular polygon with exactly seven vertices, seven edges of equal length, and seven interior angles each measuring (7−2)×180°7≈128.57°\frac{(7-2) \times 180°}{7} \approx 128.57°.

Key Formula

Each interior angle=(n−2)×180°n\text{Each interior angle} = \frac{(n-2) \times 180°}{n}
Where:
  • nn = Number of sides (for a heptagon, n = 7)

Worked Example

Problem: Find the measure of each interior angle of a regular heptagon and the sum of all its interior angles.
Step 1: Find the sum of interior angles using the polygon angle-sum formula.
(7−2)×180°=5×180°=900°(7 - 2) \times 180° = 5 \times 180° = 900°
Step 2: Divide by the number of angles to get each interior angle.
900°7≈128.57°\frac{900°}{7} \approx 128.57°
Answer: The sum of interior angles is 900°, and each interior angle measures approximately 128.57°.

Why It Matters

Regular heptagons appear on coins (like the UK 50p and 20p pieces) and in architecture. Understanding them reinforces the polygon angle-sum formula, which you will use throughout geometry courses.

Common Mistakes

Mistake: Confusing a heptagon (7 sides) with a hexagon (6 sides) or an octagon (8 sides).
Correction: Remember the prefix: "hepta-" means seven, just as "hexa-" means six and "octa-" means eight.