# S-Cool Revision Summary

## S-Cool Revision Summary

For a regular polygon with 'n' sides:

**External angle = 360/n**

For a regular polygon with 'n' sides:

**Internal angle = 180 - 360/n**

Polygon: | Number of sides: | External angles: | Internal angles: |

Triangle | 3 | 120 | 60 |

Square | 4 | 90 | 90 |

Pentagon | 5 | 72 | 108 |

Hexagon | 6 | 60 | 120 |

Heptagon | 7 | 51.4 | 128.6 |

Octagon | 8 | 45 | 135 |

Nonagon | 9 | 40 | 140 |

Decagon | 10 | 36 | 144 |

Undecagon | 11 | 32.7 | 147.3 |

Dodecagon | 12 | 30 | 150 |

## Special types of triangle

*Sides:*

**Equilateral** - All 3 sides equal and all 3 angles equal (to 60^{o}).

**Isosceles** - Two sides the same and the angles at the bottom of those sides are equal.

**Scalene** - No sides or angles equal.

*Angles:*

**Acute-angled** - All angles are acute (less than 90^{o}).

**Right-angled** - One angle is 90^{o}.

**Obtuse-angled** - One angle is obtuse (greater than 90^{o}).

*Quadrilaterals:*

**Square** - All sides equal, all angles 90^{o}, 4 lines of symmetry, rotation symmetry of order 4.

**Rectangle** - Two pais of equal and parallel sides, all angles 90^{o}, two lines of symmetry, rotation symmetry of order 2.

**Rhombus** - All sides equal, opposite sides parallel, two lines of symmetry, rotation symmetry of order 2. (Basically a square leaning over. Sometimes referred to as a diamond!

**Parallelogram** - Two pairs of equal and parallel sides, opposite angles equal, no lines of symmetry, rotation symmetry of order 2. (Basically a rectangle leaning over.).

**Trapezium** - One pair of parallel sides, no symmetry.

**Kite** - Two pairs of equal sides next to each other, one line of symmetry, no rotation symmetry, string (only joking!).

*Circles*

Circumference = 2πr

**Or, if you want to use the diameter:**

Circumference = πd

Area = πr^{2}