# Area Watch

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I'm confused!

An area is x unit . x units and the result is x

So, how come that the solution of an exercise:

1 x (3x +2 +sqrt5x) = (3x +2 +sqrt5x)

(1 being the measurement of one side of a rectangle, and the other expression in brackets the other side; no units are given)

and NOT as I maintain (3x +2 +sqrt5x)

An area is x unit . x units and the result is x

^{2}.So, how come that the solution of an exercise:

1 x (3x +2 +sqrt5x) = (3x +2 +sqrt5x)

(1 being the measurement of one side of a rectangle, and the other expression in brackets the other side; no units are given)

and NOT as I maintain (3x +2 +sqrt5x)

^{2}?
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#2

(Original post by

I'm confused!

An area is x unit . x units and the result is x

So, how come that the solution of an exercise:

1 x (3x +2 +sqrt5x) = (3x +2 +sqrt5x)

(1 being the measurement of one side of a rectangle, and the other expression in brackets the other side; no units are given)

and NOT as I maintain (3x +2 +sqrt5x)

**Jorge**)I'm confused!

An area is x unit . x units and the result is x

^{2}.So, how come that the solution of an exercise:

1 x (3x +2 +sqrt5x) = (3x +2 +sqrt5x)

(1 being the measurement of one side of a rectangle, and the other expression in brackets the other side; no units are given)

and NOT as I maintain (3x +2 +sqrt5x)

^{2}?Rectangle area = width x height.

You have a width of 1 and the height is other ugly expression involving x. So the area is just ...

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(Original post by

Because a rectangle isn't a square!

Rectangle area = width x height.

You have a width of 1 and the height is other ugly expression involving x. So the area is just ...

**davros**)Because a rectangle isn't a square!

Rectangle area = width x height.

You have a width of 1 and the height is other ugly expression involving x. So the area is just ...

Not to the square?

a line is linear

a 3D objedt is to the cube

Surely any surface (area( has to be to the square whatever units you use.

i would be grateful if you couldd explain in full your reasoning.

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#4

(Original post by

Not to the square?

a line is linear

a 3D objedt is to the cube

Surely any surface (area( has to be to the square whatever units you use.

i would be grateful if you couldd explain in full your reasoning.

**Jorge**)Not to the square?

a line is linear

a 3D objedt is to the cube

Surely any surface (area( has to be to the square whatever units you use.

i would be grateful if you couldd explain in full your reasoning.

area = width x height

If your sides were 1 unit and 6 units then the area is ,

**not**

If your sides were 1 unit and x units then the area is ,

**not**

If your sides were 1 unit and then the area is ,

**not**

Simply apply the same reasoning to your example.

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#5

**Jorge**)

Not to the square?

a line is linear

a 3D objedt is to the cube

Surely any surface (area( has to be to the square whatever units you use.

i would be grateful if you couldd explain in full your reasoning.

cm^2 or m^2 or whatever

But, as you point out there are no units mentioned in this question

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Hi

We are talking about different things... and it's probably my fault.

of course 6x 6 = 36 but if it an area it is 36 something

In this case they give no units but the result has to be to something (no unites) squared

The fact that we are talking about an area forces the result to have units

So, the next question is how should that be stated amthematically?

Maybe (3x +2 +sqrt5x)

with a note u=units

But, YES, I was wrong... although the "right" result with no indication of units squared is also wring, as far as I am concerned.

We are talking about different things... and it's probably my fault.

of course 6x 6 = 36 but if it an area it is 36 something

^{2}whether it is meters, cm, or broom handles.In this case they give no units but the result has to be to something (no unites) squared

The fact that we are talking about an area forces the result to have units

^{2}even if the problem does not mention them.So, the next question is how should that be stated amthematically?

Maybe (3x +2 +sqrt5x)

^{u2}with a note u=units

But, YES, I was wrong... although the "right" result with no indication of units squared is also wring, as far as I am concerned.

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#7

(Original post by

Hi

We are talking about different things... and it's probably my fault.

of course 6x 6 = 36 but if it an area it is 36 something

In this case they give no units but the result has to be to something (no unites) squared

The fact that we are talking about an area forces the result to have units

So, the next question is how should that be stated amthematically?

Maybe (3x +2 +sqrt5x)

with a note u=units

But, YES, I was wrong... although the "right" result with no indication of units squared is also wring, as far as I am concerned.

**Jorge**)Hi

We are talking about different things... and it's probably my fault.

of course 6x 6 = 36 but if it an area it is 36 something

^{2}whether it is meters, cm, or broom handles.In this case they give no units but the result has to be to something (no unites) squared

The fact that we are talking about an area forces the result to have units

^{2}even if the problem does not mention them.So, the next question is how should that be stated amthematically?

Maybe (3x +2 +sqrt5x)

^{u2}with a note u=units

But, YES, I was wrong... although the "right" result with no indication of units squared is also wring, as far as I am concerned.

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(Original post by

You are writing an expression you do not need a unit

**TenOfThem**)You are writing an expression you do not need a unit

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#9

(Original post by

That's where I disagree. This was not just expressions put together, They were the sides of a rectangle and the question asked for the area. An area must always bt to the square of the unit, even if imaginary. No units: no area!

**Jorge**)That's where I disagree. This was not just expressions put together, They were the sides of a rectangle and the question asked for the area. An area must always bt to the square of the unit, even if imaginary. No units: no area!

So if you have a side of 4cm and a side of 5cm then the area should be quoted as 20cm^2,

But if the sides are given as 4 and 5 and no units are given, then it is implicit that both linear dimensions have the same units and the area is just 20 (with the implication that this refers to squared units of the corresponding linear measure),

There's no need to add extra symbols to the result because everyone understands this convention

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Interesting discussion, though.

Many thanks, all.

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#11

(Original post by

I will let the matter rest, but I am from the times when maths were considered an exact science, and not subject to conventions.

Interesting discussion, though.

Many thanks, all.

**Jorge**)I will let the matter rest, but I am from the times when maths were considered an exact science, and not subject to conventions.

Interesting discussion, though.

Many thanks, all.

There is no requirement to put units^2 after this

If you were asked for rule for the area of a triangle you would say 1/2 bh

You would not say units^2

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(Original post by

If you were asked for rule for the area of a triangle you would say 1/2 bh

You would not say units^2

**TenOfThem**)If you were asked for rule for the area of a triangle you would say 1/2 bh

You would not say units^2

I take your point, but one thing is a formula to be used for cm, m, km , inched or whatever; the other is a definite area. If units are no longer required mathematics has become rather sloppy!

Time to go to bed here!

Good night and thank you for the entertainment.

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#13

(Original post by

I take your point, but one thing is a formula to be used for cm, m, km , inched or whatever; the other is a definite area. If units are no longer required mathematics has become rather sloppy!

Time to go to bed here!

Good night and thank you for the entertainment.

**Jorge**)I take your point, but one thing is a formula to be used for cm, m, km , inched or whatever; the other is a definite area. If units are no longer required mathematics has become rather sloppy!

Time to go to bed here!

Good night and thank you for the entertainment.

When area is seen as something concrete - the space inside a 2D shape - with a value - then units are relevant

When we extend the concept into the abstract - use algebra to give general expressions - the units are not relevant

Let me ask you this - if you were finding the area under a curve what units would you insist on - what if the curve were showing speed against time

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