Notice that while we are dividing the shape into equal size / shape pieces or tiles - there are a small number of pieces and they have straight sides and corners when assembled.
Try tiling the shape with an even multiple of 4 tiles. Being honest when I solved this problem my first attack was us use triangles, which worked and the logic is the same, but it leads to too large a solution.
Using squares we tile the shape with an even multiple of 4 square tiles. It is fairly obvious that 8 tiles will not map the corner of the shape. So we try 12, which is an even multiple of 4 and 3, which does enable a corner tiling. That leads to the answer shown left.