SECTION 02
The Polygon Gallery
Each polygon is named after its number of sides. Hover a plate to enlarge the figure, and read off its sides, diagonals and total interior angle measure.
Triangle
3 sides • 180° total
0 diagonals
Quadrilateral
4 sides • 360° total
2 diagonals
Pentagon
5 sides • 540° total
5 diagonals
Hexagon
6 sides • 720° total
9 diagonals
Heptagon
7 sides • 900° total
14 diagonals
Octagon
8 sides • 1080° total
20 diagonals
Nonagon
9 sides • 1260° total
27 diagonals
Decagon
10 sides • 1440° total
35 diagonals
Counting diagonals
From each vertex you can draw a diagonal to every vertex except itself and its two neighbours, and each diagonal is counted twice — once from each end.
Number of diagonals = n × (n − 3) ÷ 2
Quadrilateral: 4 × 1 ÷ 2 = 2 · Pentagon: 5 × 2 ÷ 2 = 5 · Hexagon: 6 × 3 ÷ 2 = 9