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Kim and Linda Katwijk
I should have paid more attention in math class. I had no idea back then how often I would need the skills my teachers were trying to pound into my thick head. Now as a deck designer and builder, I use geometric shapes all the time. Squares, rectangles, triangles, octagons, hexagons, pentagons, circles, and ovals are the building blocks of the artistic decks that I design and sell every day. Having a working knowledge of how to lay these shapes out is essential. In the interest of improving the Deck Building Industry, I will share with you my cheat sheets for all the geometric shapes.
Let's cover the basics. 1st) How to lay out a line at 90 degrees from a baseline. You will use 3, 4, and 5 feet (or any multiple of them, say 6, 8,10 or 9, 12, 15). Now, starting with a baseline, set two pins 3 feet apart along the baseline. (See drawing 1) From the first pin, use your measuring tape to pull a 4-foot arc. From the second pin, pull a 5-foot arc. Where the two arcs cross is the point that is 90 degrees off the baseline from the first pin.
2nd) To check that a square or a rectangle is square & true, measure diagonally from corner to corner then again from the other two corners. The two measurements should be the same.
3rd) For octagons, hexagons, and pentagons there is a fraction associated with each shape that will enable you to do the calculations necessary for laying them out. (See drawing 2) I use the octagon shape quite often. How do I get a perfect octagon? Let's say the height of the octagon needs to be 10'-4" (A). Before I begin laying it out, I will do my calculations. To find the length of the sides (B), multiply the height of the octagon (A) by .414 (i.e. 10'-4" x .414 = 4'-3 11/16"). Next I multiply A by .294 and I know that C and D are 3' 7/16". Now, I can lay out my octagon on the ground. First, I establish a baseline (the bottom side). Second, I lay out the 90-degree angle (the right side). Third, I lay out a 10' 4" square from my two lines and check that it is square and true. Next, I measure 3' 7/16" from each corner pin each direction (C & D). I check the length of each side (B) to make sure they are 4' 3 11/16". And there is my perfect octagon!
The pentagon and the hexagon are done the same way except that you will lay out a rectangle instead of a square by finding the measurement for E (see drawing 2).
Now let's say that you will be adding an octagon to an existing deck. You know that the side measurement needs to be 5'-3 5/8". How big will this octagon be? To find the answer, divide the 5'-3 5/8" by .414 and you will see that the octagon will be 12'-9 11/16".
For any of the geometric shapes (drawing 2) if you know the height measurement (A), you will multiply it by the fraction given for that shape to find out the side measurements. If the side measurement (B) is known, you will divide by the given fraction for that shape to find out the height. (If you do not own a construction calculator, chart-A will help by giving the decimal fractions for inches.)
4th) Ovals or true ellipses are very useful in deck designs. They give gentle sweeping front edges and tight curving sides. To draw them on the job site is easy once you know how.
Let's say you want an 18' wide x 10' high oval to be 17 feet from the house. Start with a string line 12 feet off the house running parallel with the house. The string line will be the long axis or the width of the oval. (See drawing 3) Drive a stake to mark the center of your oval on the string line. From this center stake measure ½ the height of your oval (five feet in this example) away from the house. This will be the top of the oval's outside edge.
The formula is:
Stake Distance (from center) = √ (½ width x ½ width) - (½ height x ½ height) (This √ symbol is a square root sign.) Wire Length = (Stake Distance x 2) + width of the oval
Example for 18' x 10' oval:
Stake Distance = (9' x 9') - (5' x 5') 81' -- 25' = 56' √56' = 7' 5 13/16" Wire Length = 7' 5 13/16" x 2 14' 11 5/8" + 18" = 32' 11 5/8" (tied in a loop)
From the center stake of the oval drive two stakes 7' 5 13/16" along the string line. Measure 9' from the center stake both directions along the string line marking the outside dimension of the oval. Now add 4" to the wire length for tying. That means 33' 3 5/8" of tie wire. Bend the wire 2" at each end, tying the wire together to form a loop. Hook the loop of wire over both stakes. Check the outside dimension at your string line and again at the mark that you made at the top edge of the oval. If these three match up, your wire is perfect. Tighten or loosen the wire loop as necessary. Now, using the wire as a guide, draw the oval keeping the wire tight.
Geometrically speaking, you are now equipped with the tools needed to create artistic decks to your heart's desire!
Until next time, keep your math skills sharp and your deck shapes interesting!