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 with height

$T=\frac{a{h}_{a}}{2}=\frac{b{h}_{b}}{2}=\frac{c{h}_{c}}{2}$
$T=\frac{ab\cdot sin\gamma }{2}=\frac{bc\cdot sin\alpha }{2}=\frac{ca\cdot sin\beta }{2}$

Area of a triangle - Heron's formula

Area of a triangle using coordinates of points

$T=\frac{1}{2}\mid {x}_{1}\left({y}_{2}-{y}_{3}\right)+{x}_{2}\left({y}_{3}-{y}_{1}\right)+{x}_{3}\left({y}_{1}-{y}_{2}\right)\mid$

or using a determinant

$T=\frac{1}{2}|\begin{array}{ccc}{x}_{1}& {y}_{1}& 1\\ {x}_{2}& {y}_{2}& 1\\ {x}_{3}& {y}_{3}& 1\end{array}|$