(Originais Teachy 2024) - Question Hard of Mathematics

During the construction of an art project promoted by a school, a group of 6th-grade students decided to create a large geometric mosaic in the shape of a chessboard in a nearby square. The mosaic will be composed of square ceramic pieces, all of the same dimension and side 'L'. To optimize the use of the pieces and ensure that all lines of the chessboard are continuous straight lines, the students decided to organize the pieces in such a way that each side of each square touches perfectly the side of two other squares. Considering an initial arrangement where a central piece is surrounded by three other pieces, forming a central 'X', and that the final project must have an even number of rows and an even number of columns of pieces, the students need to calculate the exact quantity of 'L' pieces needed to compose the mosaic. Knowing that the square has a rectangular shape and that the mosaic must occupy exactly half of the square's area, what is the minimum quantity of 'L' pieces that the students need to complete the mosaic considering that no piece is broken or cut?