Circle:

It's a 2D shape, whose all points on the shape are at a fixed point. Distance between these points and center are equal to each other. If you take a string of fixed length and rotate it about a fixed point on a plane, then each point on the string will make different circle. The fixed point of rotation will be called as center and the distance between center and any point on the string (based on which circle you are considering) will be called as radius of that particular circle. 

Formulae of circle:
Given, radius of circle is r and center of circle is on the origin. 
  1. Diameter of circle: d=2r 
  2. Perimeter or circumference of circle: c=2 \pi r 
  3. Area of circle: A= \pi r^2 

Semi circle:

If you cut a circle along it's diameter then we will get a semi circle. 

Formulae of semi circle:
  1. Perimeter or circumference of semi circle: c =(\pi r+ 2r ) = r(\pi +2) \approx 5.1416r
  2. Area of semi circle: \frac{1}{2} \pi r^2