Hi everyone, I'm trying to calculate the approximate size of my wolf's territory (in miles or square miles). I know that the hex's diameter is 750 meters but I'm not sure what's the most accurate way to calculate a territory's diameter into a "real-life" wolf territory size. =-)
If this is any help here's my current territory! (I was never the best at math lol)
Calculating territory sizes
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Calculating territory sizes
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Re: Calculating territory sizes
Yellowstone wolf territories average 300km² in real life, which is more than 6 times larger than the entire game map, but you can still calculate your territory size game-wise:
The Slough Creek game map is 7km by 7km (so 49km²), and each hex as noted by the map is 750m or 0.75km in diameter. Assuming the territory hexes are regular hexagons, we can split it into 6 equilateral triangles whose sides are half the diameter, thus our triangle's base b is 0.75km/2 = 0.375km. Since our hexagon is regular and its interior triangles are equilateral, we know that the triangle's angles are all 60° or π/3 radians. To get the area At of one triangle, we can use the formula At = (1/2)bh, where h is the height of the triangle. We can get this height using tan(π/3) = h / 0.1875, and our height comes out to be 0.3248km, so our triangle's area is At = (1/2)(0.375km)(0.3248km) = 0.0609km².
So, the area of one territory hex Ah is these 6 triangles' areas put together. Ah = 6(0.0609km²) = 0.3654km². This converts to 0.1411mi².
As you have a territory of 27 hexes, your territory is approximately 9.8658km² (or 3.8097mi²).
The Slough Creek game map is 7km by 7km (so 49km²), and each hex as noted by the map is 750m or 0.75km in diameter. Assuming the territory hexes are regular hexagons, we can split it into 6 equilateral triangles whose sides are half the diameter, thus our triangle's base b is 0.75km/2 = 0.375km. Since our hexagon is regular and its interior triangles are equilateral, we know that the triangle's angles are all 60° or π/3 radians. To get the area At of one triangle, we can use the formula At = (1/2)bh, where h is the height of the triangle. We can get this height using tan(π/3) = h / 0.1875, and our height comes out to be 0.3248km, so our triangle's area is At = (1/2)(0.375km)(0.3248km) = 0.0609km².
So, the area of one territory hex Ah is these 6 triangles' areas put together. Ah = 6(0.0609km²) = 0.3654km². This converts to 0.1411mi².
As you have a territory of 27 hexes, your territory is approximately 9.8658km² (or 3.8097mi²).
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