Sweep line over x: collect all distinct x-coordinates from rectangle left and right edges, sort them. The union area between consecutive x's is Δx times the total y-length covered by active rectangles.

At each event x, toggle each rectangle's y-interval [y1, y2] in/out of the active set. Maintain the total covered y-length by tracking a coverage count over compressed y-intervals.

Compress both x and y coordinates for performance. Use a count array over the compressed y-segments: increment when a rectangle starts, decrement when it ends. Update total_y_covered only when a segment's count transitions between 0 and 1 or 1 and 0.