Septagon — Definition, Formula & Examples

Septagon is an alternate name for a heptagon — a polygon with exactly 7 sides and 7 angles. The name comes from the Latin word 'septem' meaning seven, while 'heptagon' comes from the Greek word 'hepta.'

A septagon is a seven-sided simple polygon. It is mathematically identical to a heptagon; the distinction is purely etymological, with 'septagon' deriving from Latin and 'heptagon' from Greek roots. A regular septagon has seven congruent sides and seven congruent interior angles, each measuring $\frac{(7-2) \times 180°}{7} \approx 128.57°$ .

Key Formula

S = (n - 2) \times 180°

Where:

$S$ = Sum of interior angles
$n$ = Number of sides (7 for a septagon)

Worked Example

Problem: Find the sum of the interior angles of a septagon, and determine the measure of each interior angle if it is regular.

Step 1: Use the interior angle sum formula with n = 7.

S = (7 - 2) \times 180° = 5 \times 180° = 900°

Step 2: For a regular septagon, divide the total by 7 to find each angle.

\text{Each angle} = \frac{900°}{7} \approx 128.57°

Answer: The interior angles of a septagon sum to 900°. In a regular septagon, each angle measures approximately 128.57°.

Why It Matters

You will encounter both names — septagon and heptagon — in geometry courses and on standardized tests. Recognizing that they refer to the same shape prevents confusion when problems use one term or the other.

Common Mistakes

Mistake: Thinking a septagon and a heptagon are different shapes.

Correction: They are the same polygon. 'Septagon' uses the Latin root and 'heptagon' uses the Greek root. Most textbooks prefer 'heptagon,' but both are correct.