My problem is the following:

In a range I have a list of expenses per department:

Dpt Expense
a 1
b 2
c 3
a 4
c 5

Say they are in A2:B6 (excluding headers)

As you can see, one department can have multiple expenses

In another range, I have a grouping of departments by area:

Dept Area
a m
b n
c m

Say they are in A11:B13 (excluding headers)

Now, given a certain Area in cell D10, (in the example m or n), what
formula will give the total expense for that Area?

Say that D10 contains 'm', the result should be 1+3+4+5 = 13.
Say that D10 contains 'n', the result should be 2.

Of course, my model is a lot bigger and more complex, but the basic
problem is explained above.

What I am looking for is a single formula, array or not, but I do not
want to use auxiliary cells for intermediate results.

Can this be done?