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Polygons

Overview

Many-sided figures.

What is it?

Closed 2D shapes with straight sides (Pentagon, Hexagon, Octagon).

History

Archimedes approximated Pi by drawing polygons with 96 sides!

Key Idea

Sum of angles = (Sides - 2) * 180.

Practice This Topic

Concept Guide

Plain English: Poly means 'Many', Gon means 'Angle'. A polygon is just a shape with straight lines. The more sides it has, the more it looks like a circle. We name them by number: 5=Penta, 6=Hexa, 8=Octa.

Real-world example: Stop Signs (Octagon). Honeycombs (Hexagon - the most efficient shape for packing).

How to do it

  1. Count the number of sides (n).
  2. Subtract 2 (this tells you how many triangles fit inside).
  3. Multiply by 180.
  4. Result is the total sum of all interior angles.
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Common Pitfall

Counting corners wrong. An n-gon has n sides and n corners.

Word Problem
"What is the sum of angles in a Stop Sign (Octagon)?"
Reasoning: Octagon has 8 sides. (8 - 2) = 6. 6 * 180 = 1080 degrees total.

Practice Examples

Formula
(n-2)180
n = side count.