Answers:

 

1) The area of the new square is nine times that of the original square.

 

2)  Yes.  The length and width are tripled no matter what size square you start with so 3 x 3 or 9 smaller squares

      will always fit in the larger square.

 

 

 

DEFINITIONS:

corresponding sides -- sides in the same relative position in similar or congruent figures.[1]

corresponding areas - -areas of similar or congruent figures.[2]

similar polygons -- polygons that have the same shape but not necessarily the same size.  Corresponding sides of similar polygons are proportional.  Corresponding angles are congruent.[3]


 

[1] Geometry to go (p.452). (2001). Wilmington, MA:  Great Source Education Group, Inc.

[2] Geometry to go (p.452). (2001). Wilmington, MA:  Great Source Education Group, Inc.

[3] Geometry to go (p.592). (2001). Wilmington, MA:  Great Source Education Group, Inc.