# Hexagon :(

• May 12th 2007, 09:16 PM
whytechocolate01
Hexagon :(
Find the area of a regular hexagon with side 2 sqrt 3 cm. and apothem 3 cm. I really have no idea how to work this one out. Any help would be greatly appreciated! Thanks in advance!
• May 12th 2007, 09:28 PM
Jhevon
Quote:

Originally Posted by whytechocolate01
Find the area of a regular hexagon with side 2 sqrt 3 cm. and apothem 3 cm. I really have no idea how to work this one out. Any help would be greatly appreciated! Thanks in advance!

one formula for the area of a regular polygon is:

Area = (1/2)(apothem)(perimeter)

we are given the apothem, the perimeter is just the length of all the sides.

let A be the apothem, and P be the permeter.

then A = 3

and P = 6*2sqrt(3) = 12sqrt(3)

so we have,

Area = (1/2)AP
.......= (1/2)*3*12sqrt(3) cm^2
.......= 18sqrt(3) cm^2

see Area of a Regular Polygon and Regular polygon area formula for more info
• May 13th 2007, 04:55 AM
Soroban
Hello, whytechocolate!

Quote:

Find the area of a regular hexagon with side 2√3 cm. and apothem 3 cm.
Did you make a sketch?

You will find that a regular hexagon is made up of six equilateral triangles.

Each triangle has a base of 2√3 and a height of 3.

Can you finish it now?