If the cross-section area is not known then do a pencil-on-squared-paper rubbing of the end, and count the blackened squares.

Then multiply the cross-section area by the length to obtain a volume, then multiply by a density, which can be found in reference books, to obtain weight.

"Simples!ξ"

Option 2: cut off a sample. Weigh it. Multiply by the length of the section to be calculated and divide by the length of the sample.

"Simples!ξ"

as above really, cut off and weigh a one metre length of each steel section, then multiply that figure by the length of each section to find the weight.

eg.

178 x 102 beam at 19 kilo per metre, section is 12.2m long so 19 x 12.2 = 231.8 kilo

OR if the above doesn't work for you, why not simply refer to a standard steel weights table?????

There are pocket reference books available from many sources.

Google the subject to find thousands of references calculated in either metric or standard figures.

Look up (steel weight) (structural steel weights) etc

good for you! but if you don't know how to do this I question whether you are qualified to do much with the data, this is grade school geometry here guy.