Believe it or not, calculating the perimeter of an ellipse is a very difficult thing to do.....
Here's a very good approximation:
First, calculate "h" as
h = ( a - b)^2 / (a + b)^2 = (140 - 30)^2 / (140 + 30)^2 = 110^2 / 170^2 = 121/289
Then, we can use the this "formula".......the terms in the brackets comprise the first four terms of an infinite series, but these will do nicely enough for our purposes
P = pi (a + b) [ 1 + h/4 + h^2/64 + h^3/256]
Substituting in for a, b and h, we have :
P = about 591.6 ft
You can read more about this, here: https://www.mathsisfun.com/geometry/ellipse-perimeter.html
The infinite sum I referenced can be found under the part "Infinite Series 2"
i reward my self with food
