Geometry

1.Polygon Properties 

What is a Polygon?
A closed plane figure made up of several line segments that are joined together. The sides do not cross each other. Exactly two sides meet at every vertex.


Types of Polygons
Regular - all angles are equal and all sides are the same length. Regular polygons are both equiangular and equilateral.
Equiangular - all angles are equal.
Equilateral - all sides are the same length.

 

Convex - a straight line drawn through a convex polygon crosses at most two sides. Every interior angle is less than 180°.

 

Concave - you can draw at least one straight line through a concave polygon that crosses more than two sides. At least one interior angle is more than 180°.


Polygon Formulas
(N = # of sides and S = length from center to a corner)

Area of a regular polygon = (1/2) N sin(360°/N) S2

Sum of the interior angles of a polygon = (N - 2) x 180°
The number of diagonals in a polygon = 1/2 N(N-3)
The number of triangles (when you draw all the diagonals from one vertex) in a polygon = (N - 2)


Polygon Parts

 

Side - one of the line segments that make up the polygon.

Vertex - point where two sides meet. Two or more of these points are called vertices.

Diagonal - a line connecting two vertices that isn't a side.

Interior Angle - Angle formed by two adjacent sides inside the polygon.

Exterior Angle - Angle formed by two adjacent sides outside the polygon.

Special Polygons
Special Quadrilaterals - square, rhombus, parallelogram, rectangle, and the trapezoid.

Special Triangles - right, equilateral, isosceles, scalene, acute, obtuse.

Polygon Names
Generally accepted names

2.Common Geometry Formula  

3.Solids

Solids have properties (special things about them), such as:

-volume (think of how much water it could hold)

-surface area (think of the area you would have to paint)

Example: 
Volume of a Cuboid
A cuboid is a 3 dimensional shape.So to work out the volume we need to know 3 measurements.

Look at this shape.

There are 3 different measurements:

Height, Width, Length

The volume is found using the formula:Volume = Height × Width × Length 
Which is usually shortened to:V = h × w × l
Or more simply: V = hwl

In Any Order..
It doesn't really matter which one is length, width or height, so long as you multiply all three together.

Example: What is the volume:

The volume is: 4 × 5 × 10 = 200 units3 It also works out the same like this: 10 × 5 × 4 = 200 units3