This is Mahaganapati, ten-armed Ganesha with his consort. The attributes in his hands are not discernible, worn out due to centuries of worship. For information on the attributes please see another blog on Mahaganapati.

Though we refer to the accompanying Devi as his consort, Ganesha is not married. He is normally accompanied by Siddhi and/or Buddhi or Lakshmi.

So far I have not come across any mythology associating Lakshmi, Consort of Vishnu, with Ganesha. In any case, there are limited distinct features to identify his consorts.

His vahana, a mouse, is on the left of his consort. 

There are several noteworthy features in this idol. This Mahaganapati idol is from South India and unlike most of the idols from South India, the back is not worked on. Note the cobra around his belly, his long term companion. The best feature is perhaps the trunk and the way it is cast. Note the gap between the trunk and his upper body.

This is solid cast and the copper content is very high. This is probably from Tamil Nadu or the adjacent areas. It is about 7.5 cm in height. This may be dated to the seventeenth century, based on the wear.

This is a rarer form of Ganesha, Mahaganapati with consort, the trunk turning to the right)  (Balamuri or Valampuri) and the five-hooded cobra giving protection.