Question

base area and stability of some objects with different shapes

Answer 1

Stability can be defined as the ability of an  object to be in balanced state , even after applying external force it does not get disturbed.

The position of centre of gravity of an object effects stability.
A body with lower centre of gravity is more stable than the body with higher stability.
Example:1 
See the attachment 1
The car which has lower Centre of gravity is more stable than a car with greater 
stability.

Stability depends upon 
---> Base area
---> Height.

An object with greater height is more likely to topple over if slightly it is applied by external force and position is disturbed.
More base area of an object then more will be the stability of an object.

It is not good ides to stand up and lean over in a small boat. The heigh Centre of gravity of standing people makes it all too easy to tip the boat over 

Stability of an object is important:
--> In designs of vehicles like car and bus.
---> For tight rope walker 
--->Gymnastic players.
--> Designing of furniture like chair.