Question

PLEASE ANSWER QUICKLY! : There are four questions here please make sure to click through, I got the first answer from someone but they neglected to go through the photos. Oh well xD Any help is appreciated

Answer 1

Hey there :)

2 ) We know the perimeter of the regular hexagon to be 12 cm and the apothem to be $\sqrt{3}$ cm

The area formula of a regular hexagon is:
Area = $\frac{1}{2}$ × perimeter × apothem

Let us substitute:
A = $( \frac{1}{2})(12)( \sqrt{3} )$
   = $6\sqrt{3}$ 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 = $\frac{1}{2}$ perimeter x apothem
A = $\frac{1}{2}$ ( 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 = $\frac{1}{2}$ x apothem x perimeter
         = $\frac{1}{2}$ ( 5.5 ) ( 40 )
         = 110 cm²
Your answer will be the third option

5 ) The apothem of this hexagon is$9\sqrt{3}$ 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 = $\frac{1}{2}$ x apothem x perimeter
         = $\frac{1}{2}$ ( 108 )( $9\sqrt{3}$ )
         = 841 cm²
Your answer will be the first option