Whenever any school district existing by virtue of any special charter and governed by any or all such special charter or special school laws of this State, and having a population of fewer than 500,000 inhabitants, requires any lot or parcel of land situated within the district for a site for a school building or for an addition to any school building already erected and used for school purposes, or requires any lot or parcel of land situated within such school district for the purpose of a playground for school children, and the compensation for such lot or parcel of land cannot be agreed upon between the owner or owners of such lot or parcel of land and the corporate authority managing and controlling the public schools of such district it is lawful for the corporate authority of the district to acquire such lot or parcel of land and have the compensation to be paid therefor determined in the manner provided by law for the exercise of the right of eminent domain.