The most critical clue is the Gold 6 on the far-right edge. The grid is 6 cells tall. The only possible shapes for a 6 are 1x6, 6x1, 2x3, or 3x2. Since the clue is on the edge of a 6-tall grid, the only configuration that fits without leaving impossible gaps is a 1x6 vertical strip. This locks in the entire rightmost column immediately, providing a hard boundary for all other shapes.

Next, we turn to the Blue 12. On a 6x6 grid, a 12-cell shape has limited possibilities. Factors of 12 are (1,12), (2,6), and (3,4). Both 1x12 and 2x6 (horizontally) are too large for the grid. A 2x6 (vertically) would occupy two full columns, but its starting clue placement prevents this. This forces the Blue 12 to be a 3x4 or 4x3 rectangle. Given its central position at the top, a 3-wide by 4-tall rectangle is the only fit that doesn't immediately crash into other clues.

With the Gold 1x6 and Blue 3x4 in place, the rest of the puzzle falls like dominoes. The Purple 6 clue sits at the bottom, directly under the newly placed Blue rectangle. The space available is exactly 3 cells wide and 2 cells tall. This accommodates a 3x2 rectangle for the Purple 6.

The final two shapes, Red and Green, had no numbers. We solve them by seeing what's left. In the bottom-left, the Orange, Blue, and Purple shapes have created a perfect 2x2 corner. This must be the Red shape, revealing its area is 4.

On the left, the Orange 4 can now only be a 1x4 vertical strip to fill the remaining space without creating an invalid 2x1 gap at the bottom.

This leaves a 1x4 vertical space for the Green shape, defining its area as 4.