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 60o).

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 90o).

Right-angled - One angle is 90o.

Obtuse-angled - One angle is obtuse (greater than 90o).

Quadrilaterals:

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

Rectangle - Two pais of equal and parallel sides, all angles 90o, 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 = πr2