How to Use Geometry in Building a Fence Line

A precise fence line will save time and expense when you install the actual fence.

When you put in a new fence, first create a plan for it on paper and then with a fence line that you can make out of mason's line and wooden stakes. Mason's line is like twine but less stretchy, allowing it to more accurately mark straight lines and consistent distances. Two important uses of geometry in building a fence line are calculating the perimeter to make sure that you buy enough fencing material and using a simple application of the Pythagorean theorem to make sure the right angles in your fencing line are truly square.

Things You'll Need

• Ruler
• Graph paper or scale map of area to be fenced
• Wooden stakes
• Mallet
• Mason's line
• Tape measure
• Assistant

Instructions

1. Map the area you intend to fence in on a piece of graph paper or make a copy of a scale map of the area. Mark the corners of the fence and connect them with straight lines using the ruler.

2. Calculate the perimeter of the fence by adding the lengths of the sides. If the fence is to be a perfect square, simply multiply the length of one side by four. If it is to be rectangular, measure the width and length, add them together and multiply the result by two. The result will indicate how much fencing you need to construct your fence.

3. Plant stakes at two adjacent corners marked on your plan. Tie one end of the mason's line to the first stake then pull it taut and loop it securely around the second stake.

4. Play out the mason's line toward the third corner marked on your plan. Have your assistant hold a stake at the location of the third corner and pull the mason's line taut.

5. Square the corner according to the 3-4-5 rule. Make a mark 3 feet along the mason's line on one side of the stake and 4 feet along the line on the other side. Measure the distance between the marks. If it is 5 feet, the corner is at a right angle. If not, have your assistant adjust the position of the third stake until the marks are 5 feet apart.

6. Continue adding one stake at a time, squaring right angle corners according to the 3-4-5 rule until the fence line is complete.

Tips & Warnings

• The 3-4-5 rule derives from the Pythagorean theorem, which states that a^2 = b^2 + c^2 for a right triangle with sides a, b and c. A right triangle with sides 4 and 3, therefore, will always have a hypotenuse of 5, since 25 = 16 + 9, i.e. 5^2 = 4^2 + 3^2.

References

• FinishABasement.com: The 3-4-5 Rule for Squaring Corners
• Math Goodies: Perimeter