A very special type of polysquare puzzles is the set of 'square-puzzles', where all given shapes are squares with integral sidelength.
Reference
... the town the population is spread out with 29.5% under the age of 18, 6.7% from 18 to 24, 33.6% from 25 to 44, 20.6% from 45 to 64, and 9.6% who are 65 years of ag ...