three balls of yarn for shawl math

Hello! Thanks for stopping by today. 

Classic tale of woe, a beautiful yarn that was knit up into something I just don’t wear.  The solution of course is to gift it to someone else who will enjoy it, but this is just not gift worthy.  The yarn is too pretty to waste. Instead, I am repurposing it.  

I love this yarn and decided to make it into another shawl which I love, the East Bay Bicycle Shawl from my upcoming book #CozyCoastalKnits.  To figure out how big my finished shawl can be, I am going to use some math so bear with me. 

The original is 96” wide x 42” deep and used 900 yards of Darn Good Yarn Lace Weight Silk.  If I work at the same gauge or close to it, how far will my 300 yards go? It’s roughly a third of the yarn so it will be a third of the size.  Simple math would tell me 96/3 and 42/3 are my finished dimensions, 32 wide x 14 deep. Not so fast!  It doesn’t work that way on a triangle.  

First we need to know the total area that 900 yards will cover.  Since it’s a triangle we’ll use the standard (Wingspan x depth)/2 which is 2016 square inches. 

Since we have 1/3 the yarn this is the number we want to divide by three, 2016/3 = 672 square inches,

Now we solve for the width and depth using this as our final size, 672. The original is roughly twice as wide as it is deep so instead of solving for both numbers we can just solve for one, D because D+D=W or 2D=W now we have a new equation…. (2D x D)/2=672

Solving for D we get 26. Now I know the general size of my new shawl using my much loved last skein of Darn Good Yarn Silk Lace Weight yarn will be approximately 52” wide x 26” deep, more than enough for cruising down the East Bay Bicycle Path this Summer when it’s too hot out for the original version. 

area of triangle
how to find out how big the piece can be

Questions? Feel free to ask. I’m here to help. 



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