How do you check if a coordinate $(x,y)$ is inside or on the perimeter of a cross

Question

$1.$ How do you check if a $(x,y)$ coordinate is inside a cross?
$2.$ How do you check if a $(x,y)$ coordinate is on the perimeter of a cross?

The cross is like a medical sign. The cross will have $12$ points describing its shape.

$(3, 10), (1, 10), (1, 8), (3, 8), (3, 6), (5, 6), (5, 8), (7, 8), (7, 10), (5, 10), (5, 12), (3, 12)$

Is there any formula?

Answer 1

The interior is the union of two overlapping rectangles. One has opposite corners $(1,8),(7,10)$ the other has opposite corners $(3,6),(5,12)$. So we have $(x>1\text{ and }x<7\text{ and }y>8\text{ and }y<10)$ or $(x>3\text{ and }x<5\text{ and }y>6\text{ and }y<12)$.

The boundary is the union of 12 line segments: $(x=1\text{ or }x=7)\text{ and }8\le y\le 10$, $(y=6\text{ or }y=12)\text{ and }3\le x\le 5$, $(x=3\text{ or }x=5)\text{ and }(6\le y\le8\text{ or }10\le y\le 12)$, $(y=8\text{ or }y=10)\text{ and }(1\le x\le 3\text{ or }5\le x\le 7)$.