In trying to work with T5 on a project for my own world building (One player wants to play a High Noble (someone with a land grant per T5), I ran into an oddity...
Some time back, I ran into a quick and dirty formula for calculating the area of a hex. Simply put, if you measured from side to side of a hex (ie, a line drawn from the center of one side, through the center of the hexagon, and to the other side at the center of the line), you could estimate the area of the hex as follows:
Find the width from face to face, and multiply that by 0.866, then multiply the two together to get your area.
For example, if your hex is nominally 25 miles wide from face to face, its area will be 25 * (25 * 0.86 = 21.5) = 537.5 square miles.
In digging deeper, I had to get the formula other than the one given above as:
Area of a hexagon is (3*(3^.5))/2 * length of Sides^2
An apothem (the line from the center of the hexagon making a perpendicular line bisecting the side of a hexagon) is = Sides/2tan(180/N) where N is number of sides in polygon (6 for a hexagon).
When you don't know the LENGTH of the sides of your hexagon, but the length of the Apothem, then the formula becomes:
Length of Sides = 2 * Tan(30) * Apothem length
Final formula then becomes:
3*(3^.5))/2 * (apothem*2*tan(30))^2
(note: if using excel, you have to use (tan(radians(degrees)) to get the proper tangent value in degrees.)
So, why all this background?
Page 693 of Traveller 5th edition has this to say about fief hexes:
"Outright Ownership of one Local Hex (approximately 65 square km= 6500 hectares= 16,000 acres)."
Elsewhere, it has this to say about local hex on page 459...
"Mapped In Hexes. The Traveller Mapping System defines a hierarchy of mapping hexes: the 1000 km World Hex; the 100 km Terrain Hex; the 10 km Local Hex; and the 1 km Single Hex."
This on page 421:
"Hex Size. Hex size (or hex diameter) reflects the distance from the center of a hex to the center of an adjacent similarly sized hex. Hexes are universally even decimal multiples of meters (100 meters, 1,000 meters, 10 kilometers, and 1 km)."
This is the way to determine what the Apothum is - which would be half the distance between center of hex to center of hex (or the line that separates them from each other).
So why all this attention to detail? Per Marc Miller, each "Local Hex" is a 10 km hex, which makes it a 5 km Apothem, which in turn makes the area of a 10 km hex equal to 86.60254038 square km, or 8660.254038 hectares, or 21,399.9537766255 acres - not the approximately 65 sq km or 16,000 acres.
Can someone verify this information. I'm thinking that I'm the one who had to have messed up. But when I used the simple formula for determining the area of a hexagon, it didn't match Marc's information, so I dug deeper to find the formula that I outlined above, and that matched the quick and dirty value, but still didn't match Marc's information.