Added a three sided addition. Interior depth from house is 8 1/2 feet. Interior length is 20 feet. 5/12 pitch hip cathederal roof. I would like to figure the total sq. ft. of the interior cathederal roof area with out climbing up on the scaffolding.Since the length is greater than 1/2 the width there is a “lay over” of the existing roof. I have vertically framed the “lay over” portion off, so the hip ceiling lines do not meet with in the room.
My math skills are a little rusty and would appreciate some help on how to solve this.
Thanks
Bob
Replies
a hair over 185sf
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Assuming I'm understanding your question, it's not hard. Take the square footage of the area under the ceiling in question, and multiply that by a constant that equals the ratio of the hypotenuse of the 5/12 pitch to 1 foot. For a 5/12, that's 1.083.
For a 5/12, the hypotenuse is 13 inches per foot, so 13 / 12 = 1.083. And the number of planes in the roof don't matter if the pitch is consistent.
Or you could measure from a section view of the structure.
Not quite picturing the layout you describe, but the basic math, from Pythagerus, is that the actual length -- say, if you were trying to figure a rafter length, is 1.0833 times the horizontal run for a 5/12 pitch ---
5^2 +12^2 = 169
square root of 169 = 13,
13/12=1.0833
So, measure the horizontal run from the bottom of the ceiling to the center of the peak, multiply by 1.0833, then multiply by the length along the ridgeline. Do the same for the other side of the room & add together.
If the room is symmetric front to back (I'm thinking from your description it's not), it's easier -- do the above for 1 side and double it, OR, take the total run from bottom of ceiling to bottom of ceiling across the gable end, multiply by 1.0833, then multiply by ridge length. Ends up the same.
Example:
room is 20x15' inside, 5/12 pitch. 15' dimension is along ridgeline.
10' from front wall to center, gives 10.833' actual length from bottom to peak of ceiling. multiply by 15 gives 162.5 ft^2 for front. Same for back, as it's symmetric, so total is 325 ft^2.
Is this what you were after?
Don
You can tell people must be bored, since by the time I got my answer typed up & posted, 2 others had already snuck their more succinct answers in.
Don
Normally, I'd rather do like you and teach a man to fish instead of handing him a fully cooked meal.But in this case, it was so much easier this way!;)
Welcome to the Taunton University of Knowledge FHB Campus at Breaktime. where ... Excellence is its own reward!
Thanks for all the answers. The confusing part was answered by Tomrocks with the statement "if the pitch is consistant it really doesn't matter how many planes there are."
Thanks again to all.
Bob
If you have a 5/12 roof over a given floor area, the square footage of the roof remains the same, whether it's a shed roof, gable, or hip roof.