This room has been filled with carpets, thirty of them. Each has a number inside precisely equal to its area. Find the carpets!
A lot of the numbers in the top right are semiprimes with one factor larger than the grid's height of 27, so the corresponding rectangles can only be entered in one shape and orientation. Combined with their relative positions (other numbers serve as blockers for a given number's rectangle in Shikaku), this constrains them and neighbouring rectangles to a one-dimensional position space, as well as solving a few rectangles:
Since all the small rectangles must partition the large rectangle in Shikaku, the rectangles discussed in the previous section can be easily solved, along with the 14 one:
The highlighted cells can only belong to the 65 rectangle. Similar reasoning solves the top-left corner:
Now the 69 rectangle, also a semiprime, is constrained to one orientation and a one-dimensional position space. The rest of the puzzle can be eyeballed easily: