Question

Find the area of a regular hexagon with sides 2 cm long. Leave your answer in simplest radical form, area of similar hexagon but with a side length of 8 cm long.

Answer 1

Area of a regular polygon = NAS/2
where
N=number of sides
A=apothem
S=length of one side

Area of hexagon of side 2 cm

`=NAS/2`

`=6(2√(3)/2)(2)/2`

`=(3/2)(√(3))(2^2)` 2 is the length of one side

`=6\sqrt3=10.392` cm^2 to 3 decimal places.

Area of hexagon of side 8 cm

`=NAS/2`

`=6(8√(3)/2)(8)/2`

`=(3/2)(√(3))(8^2)` 2 is the length of one side

`=96\sqrt3=166.277` cm^2 to 3 decimal places.