formulas to add cells based on multiple conditions

I am looking to automate some addition formulas. I have a table created already, with the first column being "area ID", and 4 columns with other values that correspond to each area ID. In the table to the right, I would like to manually list the IDs to be used. Then have formulas automate the math to add up the corresponding cells.

In the example attached, the first combination of IDs is listed in column J. Below that, I have added up the cells for each category that correspond with the IDs included. Then in column K, the same situation, but a new set of IDs. I could have up to 100 combinations of area IDs, so if there is a way to automate this, that would be amazing.

Thank you!