Not sure how you get that. Let's assume that memory is allocated in sizes that are multiples of 4, and length-prefixed strings have a 4 byte length prefix.

  str len:    c-str bytes:    size-prefix bytes:  difference:
  1           1+1 (4)         4+1 (8)             4
  2           2+1 (4)         4+2 (8)             4
  3           3+1 (4)         4+3 (8)             4
  4           4+1 (8)         4+4 (8)             0
  5           5+1 (8)         4+5 (12)            4
  6           6+1 (8)         4+6 (12)            4
  7           7+1 (8)         4+7 (12)            4
  8           8+1 (12)        4+8 (12)            0

So, for example: "ABCDE" as a C-style string would require 5 bytes for the string plus one for the null terminator, which would be satisfied by an allocation of 8 bytes. An equivalent length-prefixed string would require 4 bytes for the prefix plus 5 for the string, which would then be rounded up to 12.

The only time the size-prefixed variant doesn't require more memory is when the string length is a multiple of 4. So the length-prefixed version requires an additional 3 bytes on average.