IMHO the output of cat /proc/partitions has more details (while it misses some other ones )
For once you have an exact number of blocks used (and no "vague" and possibly incorrect "Mb" sizes).
Let's take partition "nanda" it was given as 16 Mb and partition #0,
The new command tells us that it it partition #93/0 (major/minor, whatever that means) and that it is made of 16384 blocks (which implies that each block is 1024 bytes (16*1024*1024=.16777216 and 16*1024=.16384) and that the Mb are "real" Megabytes (the thingy that should be called accordingly to the "wrong" but current standard Mebibytes)
If you take partition "dn-0", it was given as 40 Mb an partition #0 (i.e. seemingly overlapping the other partition "nanda" which was also partition #0).
The new command tells us that it is instead partition #254/0 (which allows us to distinguish them) and that it has 41611 blocks which are NOT 40 Mb, as 40*1024=40960.
The good info coming from the original output are that:
and the amount of free space in those three "mounted" partitions.
Evidently your version/edition/whatever of android missed the fdisk command, cannot say if you can install/add to it some version of the fdisk.