02.28.2017. Tuesday
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 Geometry
Two-dimensional geometric shapes
⦿ Rhombus
⦿ Parallelogram
⦿ Trapezoid
⦿ Kite
⦿ Circle
⦿ Circular sector
⦿ Circular segment
⦿ Area of a Triangle
⦿ Squere
⦿ Rectangle
Three-dimensional geometric shapes
⦿ Cube
⦿ Sphere
⦿ Cylinder
⦿ Cone
⦿ Prism
⦿ Pyramide
⦿ Platonic solids
Trigonometry
⦿ Law of Sines
⦿ Law of Cosines
⦿ Trygonometry Identities of same angle
⦿ Identities for the sum and difference of two angles
⦿ Trigonometric identities of double angles
⦿ Trigonometric identities of half angles
⦿ Sum and difference of trigonometric functions
⦿ Trigonometry of right triangles
Vectors
⦿ Scalar Product of Vectors
⦿ Vector Product of Vectors
Analytical Geometry 2D
⦿ Distance between two points
⦿ Circle
⦿ Linear equation
⦿ Ellipse


Two-dimensional geometric shapes

Area of a Triangle

Area of a Triangle

Area of a triangle with height

T = a h a 2 = b h b 2 = c h c 2
T = a b s i n γ 2 = b c s i n α 2 = c a s i n β 2

Area of a triangle - Heron's formula

T = s ( s a ) ( s b ) ( s c ) ,       s = a + b + c 2

Area of a triangle using coordinates of points

A ( x 1 , y 1 ) ,     B ( x 2 , y 2 ) ,     C ( x 3 , y 3 )
T = 1 2 x 1 ( y 2 y 3 ) + x 2 ( y 3 y 1 ) + x 3 ( y 1 y 2 )

or using a determinant

T = 1 2 | x 1 y 1 1 x 2 y 2 1 x 3 y 3 1 |