come in(I have a puzzled)

Source:
#include <stdio.h>
#include <ctype.h>
void main()
{
    char a[]="this is the beautiful world!";
    char b[20];
    strcpy(b,a);
    printf("char array b size is(%d),The content of b
is:%s\n",sizeof(b),b);
    if(strcmp(a,b)==0)
       printf("a equal to b!\n");
}

Now , question as follows:

1. Why "b" size unequal "a" size , but "b" can output "a" content?
2. Why "if(strcmp(a,b)==0)" is true?