Mathematics

The key is to recognize that perimeter means adding up all four side lengths, which you can find using the distance formula between consecutive vertices. Notice that some sides might have nice patterns—check if any sides are horizontal or vertical (same $x$- or $y$-coordinate), since those distances are just differences in one coordinate. For the slanted sides, apply the distance formula $\sqrt{(\Delta x)^2 + (\Delta y)^2}$ carefully and simplify any radicals by factoring out perfect squares.

The key is to recognize that perimeter means adding up all four side lengths, which you can find using the distance formula between consecutive vertices. Notice that some sides might have nice patterns—check if any sides are horizontal or vertical (same $x$- or $y$-coordinate), since those distances are just differences in one coordinate. For the slanted sides, apply the distance formula $\sqrt{(\Delta x)^2 + (\Delta y)^2}$ carefully and simplify any radicals by factoring out perfect squares.