The area of a polygon is the sum of its side lengths true or false?

 False.  

Note: The "sum of its side lengths" would be the "perimeter" / NOT the "area".

The area of a polygon can be calculated as follows:

 Area = 1/2 * perimeter * apothem ;  and is measured in "square units" ; that is:  "units² " ;  

     and the "area of a given polygon" has a much larger numeric value than its "perimeter" .

Hope this helps!

Best wishes!