How do I calculate square footage of irregular shape? Shape has 9 sides and..?

Question

Need sq. ft. of a room with an unusual shape. Try to imagine a room with 2 bay windows that do not face each other and one has more depth. Or, if that's too difficult to explain or for me to understand, I could estimate. But to do that, I would need to know how to calculate a 5 sided area. Imagine a square that has one corner cut off leaving 5 sides.

Yes, I know how to calculate a 4 sided area. Thank you in advance.

Smallbiz, That made perfect sense. I already have a rough sketch on graph paper, then I'm going to draw to scale. Which leads to my next question, but I'm going to see if I can figure that one on my own first, but I'll go ahead and ask. I am designing a space in my house that is currently a kitchen with eat in area open to a sitting area. I'm going to redesign the whole space and remodel, but the area is irregular so I'm working hard:-) The question:

The graph paper I have is 1/4" squares and the sheets are 16"x10" of useable space. So, 4 squares per inch. Space is rectangle and in longest areas are 20'x33' I don't have any special rulers or tools and I want make a to-scale sketch that fits on one page. It doesn't have to be perfect, just close enough. For the record I have a computer program that does this, (Smartdraw) but I enjoy drawing and figuring these things out. I was never good at math.

How many squares on my graph paper to equal one foot, and still fit on one page?

I was out of room to say thanks and I am going to check out all the links soon.

Parrots...and everyone...thanks to you too, that does make perfect sense. Will anything matter if my angles are off? Space is not really an issue, it is placement of cabinets, where to lay tile and where to lay carpet, and things such as that. Also things like, is the fridge too close to the island? Etc. Basically the kitchen area is currently designed with the cabinets in a U shape. I want an island kitchen. With the odd shapes of walls and the unusual edge of where the carpet ends and tile begins, along with too many windows and a big ugly hearth, it makes this new design a challange. I really need HGTV to knock on my door and do it for me! But, since that's not likely, I'm continuing on...

Answer 1

okay, here is how i would go about that, for what it is worth.
first, i would imagine the room as a square or rectangle excluding the odd out windows. i would think of what the room would look like if they hadn't put in the bay windows and it was just a square or rectangle...meaning i would take the square or rectangle measurements of the room. say 12 x 12 room is 144 sq ft.

next, i would go to one of the bay windows, and imagine cutting it into a square or rectangle say from the middle glass window pane only, and i would get the measurement of that. say 4 x 4 = 16 sq. ft. i would get that measurement from where the original wall would have been and the depth of the bay window. just put down a yard stick or a broom to imagine that wall still being there and take a measurement from where the wall would ahve been to the middle wall of the bay window.

okay, now from here, i would get myself a carpenter's triangle and see what the angle would be of each of the triangular areas would be of the other 2 side windows of the bay. please know that if you get lucky and they are set at 45 degree angles, then if you put the 2 sides together (left and right facing the windows, hopefullly) , that, too makes a square. for example, if the left window is at a 45 degree angle or what they call a 45 45 90 triangle, then that is like half of a square if you were to imagine a square cut caddy cornered in your head. that means that if you put the left and right triangle together, it makes a square. IF YOU GET THAT LUCKY, you can take the measurement from the edge of the bay window from the left wall to the start of the middle where you measured earlier and got the square, if that makes sense.

that will work for each of the bay windows. so, let's say it was a 45 degree window on the left of and the right side of each of the bay windows. and say that those windows are slightly smaller than each of the middle windows....say 3 x 3 = 9 square feet with 4 1/2 square feet for each bay triangle.

OKAY, NOW... add:
9 sq ft. for the first bay window left and right only
9 sq. ft. for the second bay window left and right only
16 sq. ft. for the middle section of the first bay window
16 sq. ft. for the middle section of the second bay window
144 sq. ft for the rectanglular or square section of the room

all that equals 194 sq. ft.

dang, that was complicated. i so hope you understood what i was trying to say. i am imagining a rectangular room with a bay window on one wall and a bay window on another wall, and that neither of the walls with the bay windows face each other. that gave me 9 sides.

ok, now, on a different note, if each of the bay windows are NOT on 45 degree angles...say they are on 30 60 and 90 degree angles. not that is a whole different story. then, you have to find the area of those triangles. and that formula is

area = 1/2 x base x height

say the longest point on the left side of the bay window from the edge of the wall to the middle section edge of the middle bay window section is 4 ft.
and say the depth of the bay window is 3 ft.
than we multiply 1/2 x 4 x 3 = 1/2 x 12 = 6 sq. ft.
and that 6 sq. ft. will be the same measurement for both the left and right side of that bay window. for a total of 12 sq. ft.

add that 12 sq ft. to the square measurement you found earlier from just the middle section which was 16 sq. ft.

so that bay window has 12 sq. ft + 12 sq. ft. for the other side + 16 sq. ft. for the middle section = 40 sq. ft.

IF I HAVEN'T CONFUSED YOU EVEN MORE BY NOW, then i sure hope this helps.
and if you are planning on laying some carpet or some hardwood, remember (especially with the carpet) that if you have to cut the carpet into sections, you may end up with thos odd strips that cover the lines from each scetion of the carpet.

if you are laying hardwood, remember it is far easier to get extra when you go to buy so that all of the stain or dye lots will be uniform.
and if you are buying or selling your house and wer just trying to figure out the square footage, it is better to underestimate by a few feet than overestimate.

good luck. if you have more questions, feel free to contact me via email and i will do my best to respond, if nothing else than with my phone number so i can make sure you understood all of that. i have a computer program that i can create the room if you give me the dimensions, and the program will do the math for us.

LOL.

Answer 2

Irregular Square Footage Calculator

Answer 3

First, sketch it roughly on paper and measure the length of each of the straight elements. (Just to check yourself, also measure the entire length and entire width.) If you can handle an architect's scale, (special ruler showing 1/4", 1/2", & 1" increments divided as though they were 1 foot long,) draw the room to scale. Where you have angles that are not 90 degrees, use a tool or paper to mark the angle and transfer it to the drawing. Then using tracing paper or a different color pencil, mark the spaces into regular shapes, square, rectangles, triangles, figure the square footage of each, then add up the amounts. For instance, a bay window becomes a rectangle and two triangles.
I assume you are buying floor covering. If you still aren't comfortable with your total, take it to the store where you are buying the materials and have them figure it from your measurements.

Answer 4

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Answer 5

You can divide the room into rectangles, triangles and trapeziums. Most of the area can be measured by these three simple shapes.

Answer 6

Cut the room into regular shapes.

See the link for an explanation re: lots, but it can also apply to a room.

Answer 7

You can do it using Greene's theorem:

The area is |int(x) dy| along the polygon's sides.

What you need to do is express x and y as functions of t for each side, going from one vertex to the next, and calculate the integral:

int x(t) * dy/dt dt