# Hexagon around circle

• February 7th 2010, 10:52 AM
Hexagon around circle
Hello all,

I've bought an inflatable spa pool that is 1.8m outside diameter. I want to build a hexagonal wooden frame around it to protect the structure. Each side of the hexagon should touch the pool.
What internal angle should the hexagon have and how long should each side be ?

Stu
• February 7th 2010, 11:33 AM
VonNemo19
Quote:

Hello all,

I've bought an inflatable spa pool that is 1.8m outside diameter. I want to build a hexagonal wooden frame around it to protect the structure. Each side of the hexagon should touch the pool.
What internal angle should the hexagon have and how long should each side be ?

Stu

All internal angles of a hexagon are $120^\circ$.
• February 7th 2010, 11:39 AM
Quote:

Hello all,

I've bought an inflatable spa pool that is 1.8m outside diameter. I want to build a hexagonal wooden frame around it to protect the structure. Each side of the hexagon should touch the pool.
What internal angle should the hexagon have and how long should each side be ?

Stu

First get the pool diameter.

Then, a hexagon side length is $Dtan30^o$
• February 7th 2010, 11:53 AM
Thanks all for the replies, just to make sure I've got this right...

• Pool external diameter is 1.8m
• so using dtan30º would give me
• 1.8m x 0.577 = 1.03m length of each side.
• February 7th 2010, 12:03 PM
VonNemo19
Quote:

Correct, but I'm sure that a better approximation would be: $s=1.0{\color{red}4}m$