Use the simplest script to find the latest database backup and the location.

-- To get the backup history
SELECT top 100  b.server_name ,b.database_name,b.user_name, f.physical_device_name,
b.backup_finish_date,b.backup_size /1024/1024 AS size_MB,b.type,
b.is_copy_only--,compressed_backup_size/1024/1024 AS C_size_MB
FROM MSDB.DBO.BACKUPMEDIAFAMILY F
JOIN MSDB.DBO.BACKUPSET B
ON (f.media_set_id=b.media_set_id)
--WHERE database_name='test'
--AND B.type='d'
--and b.backup_finish_date >='2018-08-02 22:37:50.000'
ORDER BY b.backup_finish_date DESC

-- To get the backup type size based on the date
select sum(size_mb )from
(
SELECT sum(b.backup_size /1024/1024)as size_mb,b.database_name,b.backup_finish_date 
FROM MSDB.DBO.BACKUPMEDIAFAMILY F
JOIN MSDB.DBO.BACKUPSET B
ON (f.media_set_id=b.media_set_id)
WHERE b.backup_finish_date between '2012-04-25'and '2012-04-26'
AND B.type='D'
group by b.database_name,b.backup_finish_date 
--ORDER BY b.backup_finish_date DESC
)as ab

You can add more conditions on where clause http://msdn.microsoft.com/en-us/library/ms186299.aspx.

Like backup Type

D = Full

I = Differential database

L = Log

F = File or filegroup

G =Differential file

P = Partial

Q = Differential partial