intersect area of two polygons in cartesian plan

Question

is possible to calculate the overlapping polygons area of two polygons in cartesian plan

coordinate:

polygon 1: $(1,1) - (2,2) - (3,3) - (4,2)$

polygon 2: $(1,0) - (2,3) - (3,2) - (4,1)$

percentual area of overlapping polygons = ?

Thanks so much!! ;-)

Answer 1

Let $$A(1,1),B(3,3),C(4,2),D(1,0),E(2,3),F(4,1).$$

Then, you want to know the overlapping area of $\triangle{ABC}$ and $\triangle{DEF}$.

• The intersection point $G$ of $AB$ with $ED$ is $(3/2,3/2)$.

• The intersection point $H$ of $AB$ with $EF$ is $(1/2,1/2)$.

• The intersection point $I$ of $AC$ with $ED$ is $(11/8,9/8)$.

• The intersection point $J$ of $AC$ with $EF$ is $(1/4,3/4)$.

Now since the overlapping area is the sum of the areas of $\triangle{GHI}$ and $\triangle{HIJ}$, we have $$\small\frac 12\left|\left(\frac 32-\frac 12\right)\left(\frac 98-\frac 12\right)-\left(\frac 32-\frac 12\right)\left(\frac{11}{8}-\frac{1}{2}\right)\right|+\frac 12\left|\left(\frac{11}{8}-\frac{1}{2}\right)\left(\frac 34-\frac 12\right)-\left(\frac 98-\frac 12\right)\left(\frac 14-\frac 12\right)\right|$$$$=\color{red}{\frac{5}{16}}.$$