WOODWORKING QUIZ for 25 May 04

[Ralph Jones]

Good Evening Friends,
Following is the quiz for tomorrow of which I will answer tomorrow morning my time.

We are going to construct a gazebo with a circumscribed diameter of 12' with 6 sides. How long will the sides be?

Respectfully,

[bitingmidge]

Well Ralph, that depends entirely on the angles of intersection and whether you want them to be equal or not.

If two of the sides were 10', the other four would be something less that 2' each I imagine.

The maths is a little easier if you are building a regular hexagon with equal sides,each side would be equal to the radius of the circle or 6' . . . so curiously the total circumference of the Gazebo would be three times the diameter of the circle.

If we convert these dimensions to the Aus version of metric as set out on another thread, I think we'd have sides somewhere around a Bradman and a bit.



P

[Robert WA]

Ralph.
The Bitingmidge is right, as well as painful.
6 equal sides, each segment angle is 360/6 = 60 degrees, 6' = 1828.8 mm radius, each segment is an equilateral triangle with each side 1828.8 mm and each angle 60 degrees.

[Ralph Jones]

Good Morning Friends,
You are both correct as in any hexagon, the segment will always be 6" for a diameter of 12" in a circumscribed structure.

So as you have stated the answer will indeed be 6'.

I grew up with a Framing square manual under my arm and if you would like the formulas for circumscribed and inscribed diameters giving the lengths of the sides, just email me and I will send them you you.

Thank you for your support.

Respectfully,