Hitung Luas dengan koordinat Titik

Hitung Luas dengan Koordinat Titik

Y0^

00|

Y1+--------*

00|00000000|

Y3|--------+--------*

00|00000000|00000000|

Y2|--------+---*0000|

00|00000000|000|0000|

00+--------+---+----+-->

00000000000X100X2000X300X

Penurunan Rumus :

Luas 1 = (1/2)(X3-X1)(Y1+Y3)

0000000= (1/2)(X3.Y1+X3.Y3-X1.Y1-X1.Y3)

Luas 2 = (1/2)(X2-X1)(Y1+Y2)

0000000= (1/2)(X2.Y1+X2.Y2-X1.Y1-X1.Y2)

Luas 3 = (1/2)(X3-X2)(Y3+Y2)

0000000= (1/2)(X3.Y3+X3.Y2-X2.Y3-X2.Y2)

Luas 1 - Luas 2 - Luas 3 =

(1/2)(X3.Y1-X1.Y3-X2.Y1+X1.Y2-X3.Y2+X2.Y3)

(1/2)[(X1.Y2-X2.Y1)+(X2.Y3-X3.Y2)+(X3.Y1-X1.Y3)]

Rumus Umum =

Luas = Abs|Sum[(1/2)(Xn.Y(n+1)-X(n+1).Yn)]|

dengan X(n+1) = X(1) dan Y(n+1) = Y(1)