Aregular hexagon with a perimeter of 24 meters is dilated by a scale factor of 52 to create a new hexagon. what is the perimeter of the new hexagon?

When a figure is dilated,
The new linear dimension (side lengths, perimeters, etc) equals the old dimension multiplied by the scale factor.
The new area will be the old area multiplied by the square of the scale factor.

For example, a square of side 4m is dilated by a factor of 11.
The new side length is 4*11=44 m.
The new area is 4^2*(11^2)=16*121=1936

So for the hexagon, 
New perimeter=old perimeter * scale factor
=24*52
=1248 metres