Question

A parallel-plate capacitor has the air as a medium between its plates and its capacitance is C. A slab of the dielectric constant K is introduced so as to fill the left half of space of the capacitor, as shown. What is the new capacitance of the capacitor?

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When the medium is air, the capacitance, where A be the area of plates and d be the separation between plates. 
When slab is introduced, the whole capacitors will break into two capacitors (with slab) and (without slab) and they are in parallel.
Here,  
and  
Thus, new capacitance is

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