Octagon

Elementary School

Definition

Steming from the greek word meaning 8. An octagon can be defined by a polygon with 8 angles and 8 sides. A regular octagon has 8 equal sides and 8 equal interal angles measuring 135° each. Think of it like a square but with 8 sides instead of 4. The internal angles of any octagon add up to 1080°.

Worked examples

\(\)Sum of interior angles\( = (8 - 2) \times 180^\circ = 6 \times 180^\circ = 1080^\circ\)

Use the polygon angle-sum formula with \(n = 8\) sides to confirm all interior angles total 1080°.

\(\)Each angle in a regular octagon\( = \frac{1080^\circ}{8} = 135^\circ\)

When all eight sides and angles are equal, divide the total by 8 to find each interior angle.

Common mistakes

\(\)Sum\( = 8 \times 180^\circ = 1440^\circ\) → \(\)Sum\( = (8 - 2) \times 180^\circ = 1080^\circ\) The formula is \((n - 2) \times 180^\circ\), not \(n \times 180^\circ\).
All octagons have sides of equal length. → Only regular octagons have 8 equal sides and 8 equal angles. An octagon can be irregular with different side lengths; 'octagon' just means eight sides.
\(\)Each angle\( = \frac{360^\circ}{8} = 45^\circ\) → \(\)Each angle\( = \frac{1080^\circ}{8} = 135^\circ\) 360° is the exterior angle sum; interior angles total 1080° for an octagon.

Where you'll use it next

You'll apply octagon properties when studying polygon angle relationships, tessellations, and symmetry in geometry, and when calculating perimeter and area of composite figures that include octagons.

Found in 1 StudyPug lesson

Mastering Polygon Classification in Geometry

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Dive into the world of polygons! Learn to identify and classify shapes, understand their properties, and discover real-world applications. Enhance your geometry skills with our comprehensive guide.

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