Calculating Area

Hi, I'm trying to find the area of a segment of a circle with a hole in the center of it (think pizza slice with a hole in the center of the pie). My drawing is composed of a couple of arcs (trimmed circles) and 2 lines to form the borders. I couldn't figure out how to find the area using AutoCAD so I have been trying to figure out the area using basic math but I'm unsure of my methods enough to worry about if its correct or not I know, I know, I'm an idiot

1st - is there a way to find this out in autocad so I don't have to use my brain??

2nd - since I did use my brain, this is what I did:

pi*r^2(outer radius)-pi*r^2(inner radius) * (1 - (border angle*2)/360) = area

The way the segment was drawn, the angle to the first border is 157.5 degrees and it's a symmetrical segment. So that is why I multiplied it by 2 to get 315 degrees and then ratio'd it to 360 degrees which gave me .875... 1-.875 = .125 and so my segment is 1/8 of a circle. so 1/8th times the circle area formula should give me the area of the segment... right?

Pedit --> Join & Close.. then List your single polyline. This will give you your area. You can use this to double-check your math.

one way is to use the BPOLY command and get the area from the properties of the poly line it creates. there are others I'm sure but this is one simple way

Thanks guys, that helped a lot. Turns out I'm not a complete idiot

Hi, I'm trying to find the area of a segment of a circle with a hole in the center of it (think pizza slice with a hole in the center of the pie). My drawing is composed of a couple of arcs (trimmed circles) and 2 lines to form the borders. I couldn't figure out how to find the area using AutoCAD so I have been trying to figure out the area using basic math but I'm unsure of my methods enough to worry about if its correct or not I know, I know, I'm an idiot

 

1st - is there a way to find this out in autocad so I don't have to use my brain??

 

2nd - since I did use my brain, this is what I did:

pi*r^2(outer radius)-pi*r^2(inner radius) * (1 - (border angle*2)/360) = area

 

The way the segment was drawn, the angle to the first border is 157.5 degrees and it's a symmetrical segment. So that is why I multiplied it by 2 to get 315 degrees and then ratio'd it to 360 degrees which gave me .875... 1-.875 = .125 and so my segment is 1/8 of a circle. so 1/8th times the circle area formula should give me the area of the segment... right?

Just because I'm bored I looked through your mathematical solution. What I found in my old formula book is that the Area should be ((pi*r(outer)^2)-(pi*r(inner)^2)) * (segmentangle/360)

If I read your description, your segment goes from 157.5 degrees to 315degrees - i.e. the segment is 45degrees. And 45/360 is also 1/8, just as (1-((157.5*2)/360)) is 1/8.

so your math was right too

thanks for confirming, Tiger!

You can also hatch the area you want to calc and then select the hatch and look at the Area value in properties.

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