Two-dimensional geometric shapes

# Area of a Triangle

## Keywords: 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

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