Find match between ranges, then sum their associated cells in a different range

I am attaching a spreadsheet containing a simple example of what I want to do and the results I want. sum with criteria.xls
In summary, I have 2 ranges.
If the value in one range's cell matches a value in the other range, I want to add an associated cell from the first range to the related one in the other range and put that result in a new range.
The formula I've tried is:

=IF(Range2=A11, Twenty10b+B11, B11)

My syntax is bad, among other things, I'm sure. Need help with this. Thanks.

something like
mind the trim you have leading space in column A

Formula:

=IFERROR(VLOOKUP(TRIM(A3),$H$3:$I$14,2,FALSE)+B3,B3)

or

Formula:

=IFERROR(SUMPRODUCT(($H$3:$H$14=TRIM(A3))*(Twenty10b))+B3,B3)

Thanks very much vlady, but could you tell me what the formula should look like without the TRIM?
The spreadsheet I will apply this formula to has already been "trimmed" with a macro and reformatted before anything will be done to it.
Thanks for your time if you have the patience. The Trim portion of this formula confuses me regarding the other functions I'm trying to figure out.

the trim "deletes/removes" spaces before/after a value. since some of your example values has spaces before them I used the trim...
If you've apply trim with macro in your original no need to put it.

A1 --> space123
trim(A1) will remove space

vlookup becomes without trim

Formula:

=IFERROR(VLOOKUP(A3,$H$3:$I$14,2,FALSE)+B3,B3)

same with the sumproduct

Formula:

=IFERROR(SUMPRODUCT(($H$3:$H$14=A3)*(Twenty10b))+B3,B3)

Great! I understand now. 'Trim-range' can replace 'range' as the function component. Good to know.
Last question: do I still need IFERROR without the trim, or can it just be IF?
Thank you! As it's getting late here, I will test your formula on my "real" spreadsheet tomorrow and report back to conclude this thread.
I appreciate your time on this.

Vlookup formula worked great with a little editing of my source column to keep the vlookup range to the left of the range values to be summed for both result columns needed. I'm very excited! Will test SUMPRODUCT tomorrow and investigate IFERROR reasoning, too. Appreciate you...