# What does it mean to find the Area (e.g. area of a circle)?

by jaja1990
Tags: circle
 P: 26 What does it mean to find the area? I've read somewhere and the person says, it means to find the space enclosed, but I still don't know what that means. I understand what area intuitively means, but not logically.
 PF Patron HW Helper Sci Advisor Thanks P: 25,521 hi jaja1990! area is a measure a measure gives a value µ(A) to any subset A, and obeys µ(A U B) = µ(A) + µ(B), for any two subsets A and B which do not overlap (see http://en.wikipedia.org/wiki/Measure_(mathematics) for more details) it could be area, or probability, or cost, or … for area, we define µ(any rectangle) to be the product of the sides of that rectangle
 P: 26 Thank you, that was a lovely answer. I won't be able to fully understand the topic in the link yet, but it's on my to-do list now. Can you explain a bit on: "a measure gives a value µ(A) to any subset A, and obeys µ(A U B) = µ(A) + µ(B)"? I understand what subset and union mean, but you didn't say what B is. Also, can you tell me how "obeys µ(A U B) = µ(A) + µ(B)" applies to finding the area of a rectangle? I hope I'm not being boring by asking these questions and reading more myself. Right now, because I'm short on time, I'm just trying to get a general idea, not delve deeply and look for exact answers.
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## What does it mean to find the Area (e.g. area of a circle)?

hi jaja1990!
 Quote by jaja1990 Can you explain a bit on: "a measure gives a value µ(A) to any subset A, and obeys µ(A U B) = µ(A) + µ(B)"? I understand what subset and union mean, but you didn't say what B is.
ooh, i should have said that B also had to be a subset, with no overlap (A intersection B is empty)

(i've now edited my previous post to correct that)
 Also, can you tell me how "obeys µ(A U B) = µ(A) + µ(B)" applies to finding the area of a rectangle?
finding the area of a rectangle isn't a problem …

we define its area to be the product of the sides …

then we use µ(A U B) = µ(A) + µ(B) to define the area of any other shape (in the same way that the ancient greeks did) …

we fill out the shape with rectangles, and add up the areas of the rectangles
P: 26
 finding the area of a rectangle isn't a problem … we define its area to be the product of the sides … ... we fill out the shape with rectangles, and add up the areas of the rectangles
Why isn't it a problem for a rectangle, while it is for others? Ummm... is it because we just take the area of a rectangle to find other areas?

 then we use µ(A U B) = µ(A) + µ(B) to define the area of any other shape (in the same way that the ancient greeks did) …
Can you tell me how this applies to a circle, for example?
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hi jaja1990!
 Quote by jaja1990 Why isn't it a problem for a rectangle, while it is for others? Ummm... is it because we just take the area of a rectangle to find other areas?
yup!
 Can you tell me how this applies to a circle, for example?
like this
 P: 26 I understand how "we fill out the shape with rectangles, and add up the areas of the rectangles" applies to a circle, I was asking about:- "then we use µ(A U B) = µ(A) + µ(B) to define the area of any other shape (in the same way that the ancient greeks did) …" Specifically, I don't understand how we choose "A" and "B", I don't know how their values would look like for a circle.
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