There are 18 words that start with 'quat'.
| quate | quatre | 
| quatres | quatorze | 
| quatrain | quatorzes | 
| quatrains | quaternary | 
| quaternion | quaternity | 
| quatrefoil | quaternions | 
| quatrefoils | quaternaries | 
| quaternities | quattrocento | 
| quattrocentos | quatercentenary | 
Note: These 18 words that start with 'quat' are found from the USA & Canada version of the tournament Scrabble word list.