Two-dimensional geometric shapes

Area of a Triangle

Keywords: 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 |