Every cell belongs to exactly one rectangle, and each rectangle contains one clue that gives its area. Start with clues that have only one rectangle that fits. After you place one, nearby clues have fewer places left.
An area-4 rectangle can be 1 by 4, 2 by 2, or 4 by 1. At the top-left clue, only the 2-by-2 shape stays on the board without covering another clue.
Before: compare all three shapes with area 4. The 1-by-4 and 4-by-1 choices each cover another clue.
After: the 4 takes the top-left 2-by-2 area. No other rectangle can use those cells.
Reduce the candidate rectangles
A candidate is a rectangle that could still fit a clue.
List shapes and positionsFor a 6, try 1 by 6, 2 by 3, 3 by 2, and 6 by 1. Then slide each shape through every position that contains the clue.Cross out blocked candidatesA rectangle cannot leave the board, cover another clue, or overlap a box you already placed.Find a cell with one possible ownerIf only one clue can cover an open cell, that clue's final rectangle must include it. Remove its candidates that miss the cell.Use corners and narrow gapsEdge cells and one-cell-wide spaces fit fewer rectangles. Check which clue could still cover them.
The clue gives area, not side length
A 6 does not mean a side must be six cells long. It may form a 1-by-6, 2-by-3, 3-by-2, or 6-by-1 rectangle. Check every shape that fits before you place it.