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jaja1990
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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.
jaja1990 said: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?
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?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
Can you tell me how this applies to a circle, for example?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) …
jaja1990 said: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?
Can you tell me how this applies to a circle, for example?
jaja1990 said:"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.
The area is the measure of the size of a surface or a two-dimensional shape. It is expressed in square units such as square meters or square feet.
The formula for finding the area of a shape depends on the shape itself. For example, the area of a rectangle can be found by multiplying its length by its width. The area of a circle can be found by using the formula A = πr², where r is the radius of the circle.
Finding the area of a shape allows us to quantify the amount of space it takes up. This is useful in many fields such as architecture, engineering, and mathematics. It also helps us to compare and analyze different shapes.
Finding the area has many real-life applications. For example, it is used in designing buildings and determining the amount of material needed for construction. It is also used in farming to determine the amount of land needed for crops and in cartography to measure the size of a piece of land.
No, the area of a shape cannot be negative. It is always a positive value because it is a measure of the space enclosed within the shape. If the shape has an irregular or concave shape, the area may be expressed as a negative value but it is still the same in terms of magnitude.