I need to write a class to a binary file, and then I need to read it back.
I have Triangle and BinaryFile classes, and some other classes.
What you are looking for is to serialize your classes/data that should be saved to file. There are several libraries that has been optimized regarding time and memory consumption for this. Would you mind using a 3rd party library?
If not, have a look at for example boost serialization, cereal or maybe even Google's ProtoBuf. I recon Cereal is a good start if you are using C++11.
If you'd like to write your own serialization you'd have to consider that for every object that has a dynamic size (such as a string), you will also need to save the object's size to the file. For more info please have a look here:
https://stackoverflow.com/a/11003590/5874704