I have downloaded a satellite image which is showing patches of forest, barren land, and snow-covered area. The question is how can i calculate forest area, barren land, rivers and ice-covered area? If forest the which types of forest ?
Lots of help topics. What have you looked at?
For example
Overview of image classification—ArcGIS Pro | Documentation
The Image Classification Wizard—ArcGIS Pro | Documentation
and perhaps Image Processing with ArcGIS | Esri Training Web Course
Is this image classified already? If not, you will first need to carry out that classification process. If you are going down that road - you really need to define / decide upon the classes you wish to identify first.
Then, you could look at using a Zonal Statistics approach to calculate % area per class type, or even use Tabulate Area. Really depends on your desired output / workflow!