A series paper sizes are defined as follows; the A0 size has an area of one square metre, and each successive size is half the one previous. Also, if an A series sized piece of paper is cut or folded on half along its width, then the piece of paper formed is the same shape as the piece you started with; this means that the paper has length and width in the golden ratio, 1.618034... to 1.
A4 paper is therefore formed by 4 successive halvings, so it has an area of one sixteenth of a square metre or 625 cm2.