You would add area of all the sides up. Now, that's literally the formula I like to consider. And, that will work for any non-circular prism, period.
Now, special formulas do exist for specific types of prisms, for instance, a rectangular prism, you could consider the formula for the area of one side, length x width, then consider there is another one of those sides, so two of them, so 2 x length x width. Then, pick another side and find that area, like width x height. And, there is another one of those, so 2 x width x height. And, likewise for length x height. There would be 2 x length x height. So, adding those up, you would have:
total area rectangular prism = 2LW + 2LH + 2WH
where L = length, W = width, and H = height
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