# Talk:Area

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Area was a Mathematics good articles nominee, but did not meet the good article criteria at the time. There may be suggestions below for improving the article. Once these issues have been addressed, the article can be renominated. Editors may also seek a reassessment of the decision if they believe there was a mistake.
Article milestones
DateProcessResult
July 22, 2012Good article nomineeNot listed

## ell or l?

The formula for the area of a rectangle uses the varible ${\displaystyle l}$ to denote length, while the formula for area of a rectangular box uses the variable ${\displaystyle \ell }$ to denote length. Is there a reason why, or can they both be ${\displaystyle l}$? —Preceding unsigned comment added by Goingstuckey (talkcontribs) 19:17, 16 April 2009 (UTC)

99% of references ti area are about sizes of countries and planets, so I put part of it in area (geometry), (I will make changes in math part of refs). Tosha

hmmm, well there are a few errors but most recognisable is the - or "minus" before each number. Please note that the - key is a minus not a mear explanation line and there for numbers displayed as -10 cand easily be confused for the actual minus 10 number, not just postive 10.

## The Areas

Hi. This article is good but needs a few changes. The derivation of the areas are not explained and neither are there any diagrams. It's not user friendly! Plus, there could also be some sums and more information on areas of prisms, pyramids etc.. When I saw this there were only two formulas for the areas under "some useful formulae" , So I've added some more.---Pujita

## Formulas Table

i've alphabetized this table, and took out all the "A"s and "An"s. it seems more user-friendly now. who ever wrote that thing above is such a dork and geek!!!!! lol. —Preceding unsigned comment added by 69.132.81.114 (talk) 22:42, 7 October 2007 (UTC)

also, since most human beings looking for the formula for the area of a circle will be looking for "circle", i put a note in the table directing them to see the formula for "disk".

--Brianbarney 02:05, 19 July 2006 (UTC)

I'd rather see this in the old form where the rows are ordered according to complexity as is most common. The table only has eleven entries and does not need to be alphabetized to be useful. I strongly feel that it was better the other way!
As for the circle entry, a circle is not a synonym for a disk. --Swift 10:19, 19 July 2006 (UTC)
i accept the veto. but maybe you can explain why the area of an enclosed circle has a special name, yet the areas of an enclosed square or triangle do not... as far as i know.
--Brianbarney 07:44, 14 August 2006 (UTC)
Thanks. I'm not aware of any other name for the area enclosed square, triangle etc. either.
I cannot, unfortunately, offer any better explanation than that there may simply be a greater need in the English language for a word representing the concept of a disk than the areas of other shapes.
If in need to distinguish the two, you can always result to using square, triangular, etc. -area. --Swift 00:38, 15 August 2006 (UTC)

## Merge area and surface area

Admittedly area can apply to non-surfaces, but there is no need to have two articles. One begins with area and the other has surface area on the second line. There is no need for this repetition. Richard001 09:47, 1 August 2007 (UTC)

We have area (geometry) as well... can we not just roll them into one? It's mainly a mathematical concept, so it would be difficult to make an article than merely summarizes the geometry article. Richard001 10:09, 1 August 2007 (UTC)

I oppose merging surface area here. Surface area is a concept in solid (3d) geometry, which makes it distinct enough from the concept of area in plane (2d) geometry to rate its own article. 18:33, 26 September 2007 (UTC)
I think it's worth mentioning that the definition of the term "area" extends beyond geometry, math, and abstract concept. To wit: I went looking for land area as an article on the concept, and got redirected to a list of countries. I tried just area and got a dab page. That led here -- an article focused on abstract geometry. Now, obviously, any formal discussion of area is going to involve the mathematical aspects at a fundamental level, but it should go beyond that, too. Unfortunately, I don't have any proper solution to propose on this -- just the additional complication. —DragonHawk (talk|hist)
I agree they are separate articles. However, the Surface area article had tried to cover the material here, but did so less completely. There was similar overlap with Surface area to volume ratio. I removed most of the material from Surface area, leaving the definition and some pointers. -Dmh (talk) 06:22, 23 April 2009 (UTC)

## SQUARE AREA

I appreciate that geometry can be very complicated, however my question, is simplistic to the extreme. The question relates to the calculation of Square Area within different Shapes where Perimeter Lengths are equal.

Logic asks, should different Shapes, which have the same Perimeter length, not have the same Area within them? This shows the logic under question: a Square with Perimeter 16 units a Circle with Circumference 16 units a Triangle with Perimeter 16 units a Parallelogram with Perimeter 16 units any Shape where Perimeter is 16 units

Although all of the Shapes are different, each of their Perimeter lengths are the same and would form a 4x4 Square Perimeter. We know that the SqRt of Perimeter length when Squared is the SQ. Area within the Perimeter. So why are the various formulae necessary to calculate Area? Why do the various formulae produce a result that disagrees with this basic logic?

Can someone explain this? --Layman1 (talk) 11:26, 11 December 2007 (UTC)

The 'shape' of the shape (i.e. the lines involved as well as their lengths and the angles at which they meet) all contribute to the area of the shape. Thus, a circle of perimeter n will encompass a greater area than a triangle of perimeter n. One can explain this visually using a grid. While all shapes with a perimeter n would form an n x n square of the same area, that would be due to the shapes having changed to the square. 82.178.149.132 (talk) 14:05, 16 December 2008 (UTC)

## Import from Surface area

I am not sure how to fit it in here, but the following table decidedly does not belong to "Surface area", where it was found. Arcfrk (talk) 08:19, 11 March 2008 (UTC)

Note: For 2D figures, the surface area and the area are the same.

Common equations for surface area (2-Dimensional Objects):
Shape Equation Variables
A rectangle: ${\displaystyle l\cdot w}$ l = length, w = width
A circle: ${\displaystyle \pi \cdot r^{2}}$ r = radius
Any regular polygon: ${\displaystyle P\cdot a/2}$ P = length of the perimeter, a = length of the apothem of the polygon (the distance from the center of the polygon to the center of one side)
A parallelogram: ${\displaystyle B\cdot h}$ B (base) = any side, h (height) = the distance between the lines that the sides of length B lie on
A trapezoid: ${\displaystyle (B+b)\cdot h/2}$ B and b = lengths of the parallel sides, h = distance between the lines on which the parallel sides lie
A triangle (1): ${\displaystyle B\cdot h/2}$ B = any side, h = distance from the line on which B lies to the other point of the triangle
A triangle (2) ${\displaystyle {\sqrt {[p\cdot (p-a)\cdot (p-b)\cdot (p-c)]}}}$ a, b and c = sides of triangle, p = half of the perimeter, or (a+b+c)/2

## Formulae 'useful'?

Some of them are not very useful. And besides, it's a subjective statement. I've changed the section heading from "Useful formulas" to just "Formulae". Leon math (talk) 22:20, 4 January 2009 (UTC)

So long as a shape does not have any concave or inverted angles the formula for the area of any other shape should be (P/4)squared were P=Perimeter. Darren Miller 30/10/2011 — Preceding unsigned comment added by 101.171.241.54 (talk) 20:05, 29 October 2011 (UTC)

Try that with a 10x10 square and a 19x1 rectangle.
10*4 = 40
(19*2) + (1*2) = 38+2 = 40
So the perimeters are the same, and
(P/4)² = 10² = 100 for both.
Are you going to say that it's irrelevant that
10*10 = 100 and 19*1 = 19 ?
I hope not.
--Thnidu (talk) 03:18, 17 January 2017 (UTC)

## Still start class?

Looks pretty good to me. I'm trying to get rid of the bolded articles in mathematics on the Vital articles page. Leon math (talk) 22:23, 4 January 2009 (UTC)

## Basics

I think "square metre (m²)" should be at the top of the Units section, no?
Should there be a note about the difference between e.g. 2 square metres and 2 metres squared?

## Content

In the subsection 'How to define area', we are told that The n dimensional analog, usually referred to as 'content', is defined by means of a measure or as a Lebesgue integral. I've never heard the term 'content' used in this way, but I'm only one person so I haven't removed it. Can anyone else back this up? Cheers, Ben (talk) 23:31, 29 March 2009 (UTC)

"Content" in that sense is fairly specialized to analysis. Similarly, the Lebesgue integral is one particular analytical definition for the integral. There are several, each of which looks like the "integral" you learnt in maths class in most cases, but handles hairy cases like the characteristic function of the rationals in its own special way. I believe the more general-purpose higher-dimensional analog is just "volume", or "n-volume" if you're specifying the particular dimension, as "4-volume" for a hypercube. But I'm a bit rusty. -Dmh (talk) 06:29, 23 April 2009 (UTC)

## where's the original?

i would just like to have the formula for figuring out the area of something, not an exact shape, lika polygon or square. thank you. —Preceding unsigned comment added by 65.103.77.114 (talk) 22:28, 6 May 2009 (UTC)

Sorry. S.O.L. There ain't none. --Thnidu (talk) 03:23, 17 January 2017 (UTC)

## Pluginless calculator

I have this page [1] which offers a handy calculator for any parameter of the various area equations. Do you agree to post it as an external link? I checked it and it complies with the external link guidelines. See you. Elpiades (talk) 03:33, 16 July 2009 (UTC)

## Populations, land area, and population density

I found mistakes concerning this information. My concern is a section of a talk page Population density. hello (talk) 17:59, 1 December 2009 (UTC)

## Still Start Class

Three sentences?! All Wikipedia editors have to say about a profound, fundamental concept in mathematics is three sentences followed by long lists of miscellaneous units and formulae? (Ok, there are three more short sentences at the end about minimal areas, but they don't say much yet. Still, it's a start!) Where is the discussion of the meaning of area? The relationship between the intuitive concept and mathematical definitions? For that matter, where ARE the mathematical definitions? Axiomatic treatment? Motivation for such treatment? How about a short history of the concept, beginning with the foundations of geometry and moving on to Euclid's treatment of area and on through calculus and modern axiomatic treatments? Put the stale lists of units and formulae at the end and include some interesting facts about area, such as relationship to perimeter and other measuring concepts. The tiny section near the end can be greatly expanded to include theorems on minimum and maximum areas under various constraints. Put it before the units and formulae. There is so much more I haven't even mentioned -- fractal areas, various area theorems, psychological concepts of area, and on and on and on.

With long and detailed Wikipedia articles on every trivial subject imaginable, it is rather inconceivable that this important article contains so very little. Here's hoping this important article moves beyond Start Class some day! --seberle (talk) 19:40, 6 April 2010 (UTC)

Jim belk: Thanks for the recent edits. That is a much improved introduction. The remainder of the article is still mostly about formulas/formulae (a consistent plural is needed--either one will do). We still need an axiomatic presentation with basic theorems. Belk's edits suggest addressing this need from two different approaches: one axiomatic, one derived from arithmetic. How is this to be organized? I'm glad the priority for this article has been increased to "high." --seberle (talk) 21:17, 15 November 2010 (UTC)

## Oriented area

There's no article with such name, so I thought it'd be nice to dwell a little bit about it here and give as it's generalization notions of determinant and integrals. What do you think about such idea? Is it sound? konradek (talk) 15:59, 28 December 2011 (UTC)

## Table?

Stumbled on this page when editing Gaussian surface. Yes I'm nitpicky, though any reason the tables have no solid rows/columns? I'm sure they were there at one point - why remove them???... Its clearer with them in so I added them back.-- 11:37, 25 February 2012 (UTC)

## Start class?

This article has come a long way in the last two years. What is the procedure for reevaluating its Start Class status? If it is still Start Class, what are the most important things that need to be added? --seberle (talk) 19:57, 8 May 2012 (UTC)

I would be happy to start a collaboration to get this up to GA, any takers? -- 17:03, 1 July 2012 (UTC)
The article has come on a way since it was last reviewed several years ago so I'm upping the rating to B.--Salix (talk): 07:15, 2 July 2012 (UTC)
Thanks. In the "List of Formulae", where should the references be? Next to the name of the solid? Next to the formula? Or somewhere else?-- 11:46, 3 July 2012 (UTC)

## GA Review

Reviewer: TheSpecialUser (talk · contribs) 07:16, 15 July 2012 (UTC) Interesting! I have done 9 reviews but haven't came across such popular topic which I loved a lot. I'll give out initial review till tonight. — TheSpecialUser (TSU) 07:16, 15 July 2012 (UTC)

To start off with, I'll give out "general fixes" (with time, I may add more problems)

General fixes
• Images need WP:ALT, thus can you add them to it. Done
• Section references: It contains a sub-section called "Notes". Well, no need of it, thus remove ==Notes== Done
• An approach to defining what is meant by area is through axioms - link Axioms  Done
• For example, we may define area as a function a from a collection M of special kind of plane figures (termed measurable sets) to the set of real numbers which satisfies the following properties: -> Area can be defined as a function from a collection M of special kind of plane figures (termed measurable sets) to the set of real numbers which satisfies the following properties:  Done
• (See, for example, Elementary Geometry from an Advanced Standpoint by Edwin Moise) - odd. Please either remove it or add it in the form of ref  Done, the user who added the ref is now inactive, but I've AGF'ed and found it on google books, adding a full citation using the cite book template.
• The are was the original unit of area in the metric system, with -> The "Are" was the original unit of area in the metric system, with;  Done
Ref fixes
• ref 11 - is a linkrot, please expand it  Done using {{Cite Journal}} template.
• ref 12 - ISBN?  Not done, not applicable.
• ref 7 - ISBN?  Done

— TheSpecialUser (TSU)

All done, at 14:26, 15 July 2012 (UTC) -  Done -- 14:26, 15 July 2012 (UTC)

Nitpicks aside, I see some pretty major organizational problems with this article. The purpose of the lead section is to summarize the major points of the body of the article; a person who skips the lead and reads the body should not miss out on anything. Currently, this is not the case. The lead attempts to provide the uninformed reader with an intuitive understanding of the concept (which is commendable), whereas the body gives a rigorous mathematical definition, and there is literally no overlap between the two approaches.

"Area plays an important role in modern mathematics." This sentence, and much of the paragraph that follows it, is completely unsubstantiated by the body of the article. Conversions does not belong in this article. Basic area formula, List of formulae, and Additional formulae are largely redundant and should merged into a single section. Minimization is blatantly incomplete, and even if it were fleshed out further, it should probably be generalized to Optimization.

Another major issue is the deficiency of sources. Much of the article is unsourced, and 13 references is not nearly enough to summarize a topic as pervasive as this one. My recommendation to the author: compile a collection of scholarly sources (e.g. math textbooks, math history books, and journal articles) and use them to rewrite the body of the article from scratch. Once that's done, trash the current lead and write a new one to summarize the new body. --Cryptic C62 · Talk 20:15, 15 July 2012 (UTC)

Thank you for your comments. I agree with most of the points, and am currently doing a major re-structuring, but would disagree with the conversion being un-necessary. How would you suggest giving the uninformed reader an intuitive view within the body of the article?-- 20:56, 15 July 2012 (UTC)
Related to Cryptic C62's complaint about sources, I think we should not be using MathWorld as a source in a good article; it has too many inaccuracies, and is better as an external link. The math.com link is even more dubious. In any case, the subject of this article is so basic that it should not be difficult to find good textbook sources for everything in it. —David Eppstein (talk) 00:00, 16 July 2012 (UTC)
I was thinking of slimming down the current lead and using it as a basic explanation, and adding a new lead summarising the whole article. (Away until monday)-- 14:06, 16 July 2012 (UTC)

My next issue would be about refs and prose. It is already stated above that the lead doesn't summarize the article and gives few new things which is not covered later in the article. I'd suggest looking at Pi and take it as an example and work on this. There are ton of things that need refs. This looks like a quick fail but I'd live to keep this open for 1 week minimum. I'd be also working on article a bit (As a reviewer, I m not restricted to do that and even if I were, I'd just boldly ignore it. Remember; Wikipedia doesn't have firm rules). I'd add few sources but I were never good at Math and thus won't be able to contribute more. It looks too tough overall to refimprove it or to establish the prose. I'd suggest the nominator to withdraw (so that I can fail it) as this issue I don't think can be addressed in 2-3 weeks. Awaiting response. — TheSpecialUser (TSU) 15:36, 18 July 2012 (UTC)

I withdraw.-- 20:22, 22 July 2012 (UTC)

## Engvar: formulas versus formulae

Some section headings (and some sentences) use the American plural "formulas", and some use the British plural " formulae". By WP:ENGVAR it should always use the one that was used first. This link [2] to the very first incarnation of the article shows that "formulas" came first. So I'm making the article uniformly use "formulas". Loraof (talk) 17:55, 29 September 2014 (UTC)

## Assessment comment

The comment(s) below were originally left at Talk:Area/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

 Geometry guy 17:49, 14 April 2007 (UTC) Upgraded to high priority. This is one of the ten most viewed mathematics articles! Jim.belk (talk) 00:25, 14 November 2010 (UTC)

Last edited at 00:25, 14 November 2010 (UTC). Substituted at 08:12, 29 April 2016 (UTC)

## BC/AD <--> BCE/CE edit war breweing?

Do we have an edit war brewing here? I just saw two edits that differ only in these. What is the official WP policy, or is there one? I did find WP:Neutral_point_of_view/BCE-CE_Debate, but haven't had time to research it further. Jimw338 (talk) 03:46, 12 September 2016 (UTC)

The policy is found at WP:ERA and essentially says that the era style should not be changed unless there is a good reason (discussed on the talk page) to do so.--Bill Cherowitzo (talk) 04:12, 12 September 2016 (UTC)

## "are" in plain text really threw me off

I think it would be prudent to embolden or italicize the word "are" used as a noun that is the archaic term for hectare and pronounced with a long 'a' sound. Perhaps even prelude it with the formal definition before using it in a sentence. Steph6n (talk) 16:42, 27 August 2021 (UTC)