Modulus functions create piecewise-defined curves that often form symmetric, closed regions. For |f(x)| + |g(y)| = k, consider all four sign combinations to get four linear equations, forming a quadrilateral (often a rhombus or rectangle). Strategy: (1) Remove the modulus by considering each quadrant separately. (2) Exploit symmetry to compute area in one quadrant and multiply. Example: |x - 1| + |y - 2| = 3 is a square (rotated 45 degrees) centered at (1, 2) with diagonal length 6, so area = (6)^2/2 = 18. For y = |$x^2$ - 4|, the curve equals $x^2$ - 4 when |x| >= 2 and equals 4 - $x^2$ when |x| < 2, creating an inverted parabolic arch between -2 and 2.