I had to look up the square footage for an acre! One acre is equal to 43,560 square feet. So, 1.25 acres is equal to (43560 sq ft / acre))(1.25 acres) = 54450 sq feet.
So that's the area in terms of square feet. The area of a square is A = s^2, where s is the side. So you want to FIRST find the length of a side of your square. That's where square roots come in! You have (54450 ft^2) = s^2, which means s = SQRT(54450 ft^2).
You actually take the square root of BOTH 54450 AND the "square feet". The square root of "square feet" is just "feet", a linear foot. So you get:
s = SQRT(54450 ft^2)
s = 233.34 ft
You have to do it on a calculator - google will do it for you, or Wolfram Alpha can do it too. There are algorithms to do square roots by hand, but I think they thankfully stopped teaching that back in the 50s.
Now you have ONE side of your yard. Your square has FOUR sides. So you want to find the perimeter, which is equal to s + s + s + s = 4s, since all sides are the same. In this case, you get:
P = 4s = 933.38 ft
So you need about 933 feet, or 311 yards, of wire to surround your field once. If you want to string, say, four pieces of wire around the fence, you'd need four times as much.
However, you said that your field is "almost square". There's a fun theorem that says that if you have two fields with the same area, and one is a square, and the other is a rectangle, the square will ALWAYS have the smallest perimeter. Think about this in an extreme case...if you squashed your 54450 square feet into a 1 foot by 54450 foot rectangular field, you'd need 1 + 1 + 54450 + 54450 feet of wire!
So, in practical terms, you'll need MORE than 311 yards of wire to surround your field once. How much more depends on how "non-square" it is.
1 acre = 43560 ft^2 = s^2
s = 208.7103256... ≈ 208.71 ft
P = 4s = 4(208.71) ≈ 834.84 ft
Approximately 834.84 ft of wire would be needed.
1 ac = 43560 sqft.
1.25 ac = 54450 sqft
approx. side of a square that measures 1.25 acres: √54450 ≈ 233.35 feet
How much fence ? 4 * 233.35 ≈ 933.4
to be safe...about 950 linear feet of fencing...
go for it.