The figure below shows a regular hexagon inscribed in a circle. The length of each side of this figure is 8 cm. Which of the following values represents the length of apothem PQ?

The answer is 4√3 or 6.3

The size of angles in a hexagon is:

[ (n-2) * 180]/6

= (720) / 6

=120°

thus the length of the apothem will be found as follows:

tan θ=opposite/adjacent

θ=120/2=60

opposite=apothem, a

adajcent=base=8/2=4

hence

tan 60=a/4

a=4 tan 60

a=6.93

Thus PQ=6.93