Boundary Math Example 4

Solution

1. 1
   Step 1: The region is a triangle with vertices at $(0,0)$, $(6,0)$, and $(0,6)$.
2. 2
   Step 2: The boundary consists of three line segments: the $x$-axis from $(0,0)$ to $(6,0)$, the $y$-axis from $(0,0)$ to $(0,6)$, and the line $x+y=6$ from $(6,0)$ to $(0,6)$.
3. 3
   Step 3: Lengths: $x$-segment $= 6$, $y$-segment $= 6$, hypotenuse $= \sqrt{6^2+6^2} = 6\sqrt{2}$. Perimeter $= 12 + 6\sqrt{2} \approx 20.49$ units.