Answer quickly! : there are four questions here make sure to click through, i got the first answer from someone but they neglected to go through the photos. oh well xd any is appreciated

Hey there :)

2 ) We know the perimeter of the regular hexagon to be 12 cm and the apothem to be  cm

The area formula of a regular hexagon is:
Area =  × perimeter × apothem

Let us substitute:
A = 
   =  cm²
Your answer will be the second option

3 ) We know the value of the apothem to be 16.9 cm and the side length to be 14 cm

The perimeter of this octagon is:
P = 8 x side
   = 8 x 14
   = 112 cm

Area formula of a regular octagon is
A = perimeter x apothem
A =  ( 112 )( 16.9 )
   = 946 .4 cm²
Your answer will be the last option

4 )  The apothem of the regular pentagon is given to be 5.5 cm and the side is 8 cm

The perimeter of this pentagon is:
P = 5 x side
   = 5 x 8
   = 40 cm

Area formula of a pentagon is:
Area =  x apothem x perimeter
         =  ( 5.5 ) ( 40 )
         = 110 cm²
Your answer will be the third option

5 ) The apothem of this hexagon is cm and the side is 18 cm

The perimeter of the hexagon is
P = 6 x side
   = 6 x 18
   = 108 cm

The area formula of a regular hexagon is
Area =  x apothem x perimeter
         =  ( 108 )(  )
         = 841 cm²
Your answer will be the first option

In order to have an infinite number of solutions, it should be that the two equations are identical. Therefore, I believe the correct answer is option c. The value of b should be 6. Hope this answers the question.