# Math Is Fun Forum

Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

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## #1 2006-07-22 00:29:12

RauLiTo
Member
From: Bahrain
Registered: 2006-01-11
Posts: 142

### the area of the square and rectangle

there is a rule to get the area of the square or rectangle or anything with four ...
which is : half the product of the digonal X sin !
in the square sin 90 = 1
so its : half the product of the diognal

can anyone tell me where did they bring that rule from ?

ImPo\$\$!BLe = NoTH!nG
Go DowN DeeP iNTo aNyTHinG U WiLL FinD MaTHeMaTiCs ...

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## #2 2006-07-22 03:11:07

RauLiTo
Member
From: Bahrain
Registered: 2006-01-11
Posts: 142

### Re: the area of the square and rectangle

maybe i didnt say it clear thats why no one answered me
okay here you are :

prove that this is right :
The area of a general irregular quadrilateral is equal to half the product of the diagonals and the sine of the angle between them.

ImPo\$\$!BLe = NoTH!nG
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## #3 2006-07-22 03:14:05

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

### Re: the area of the square and rectangle

It's simple:
Let the rectangle is ABCD and it's diagonals intersect in E.
Then S(ABCD)=S(AEB)+S(BEC)+S(CED)+S(DEA).
Now use that S(XYZ)=xy sin Z and apply to all triangles.

IPBLE:  Increasing Performance By Lowering Expectations.

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## #4 2006-07-22 04:25:37

RauLiTo
Member
From: Bahrain
Registered: 2006-01-11
Posts: 142

### Re: the area of the square and rectangle

what s mean ?! can you explain more man if you dont mind

ImPo\$\$!BLe = NoTH!nG
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## #5 2006-07-22 05:07:47

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

### Re: the area of the square and rectangle

well that rule is a little messed up

you say its half the product of the diagonals, and the angle between them, but there are two distinct angles (par the square) for the angle between the diagonal, so that doesnt make sense

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## #6 2006-07-22 05:27:36

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

### Re: the area of the square and rectangle

Sorry. I use S for the area.
And tha angle between two straight lines is the smaller of the two (i think...).

IPBLE:  Increasing Performance By Lowering Expectations.

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## #7 2006-07-22 06:02:51

RauLiTo
Member
From: Bahrain
Registered: 2006-01-11
Posts: 142

### Re: the area of the square and rectangle

sorry for bothering you guys ... !!!
but i really didnt get it until now ... anybody else can help ?! maybe with drawing it will be easier to explain it thanks thanks thanks again !!!
anybody ?

ImPo\$\$!BLe = NoTH!nG
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## #8 2006-07-22 08:24:12

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: the area of the square and rectangle

you say its half the product of the diagonals, and the angle between them, but there are two distinct angles (par the square) for the angle between the diagonal, so that doesnt make sense

Krassi is right.  Think how it this way.  Jim and Bob are on earth, and Jim is 10 feet to the left of Bob.  When I ask you how far Jim is from Bob, you would say 10 feet.  You wouldn't say "The circumfrence of the earth minus 10 feet", which is also technically correct.

The same is true when we talk about angles.

As for the original question, it comes out of vector geometry.  Do you know what a dot product and a cross product is?  Do you understand vectors?

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #9 2006-07-22 08:27:45

RauLiTo
Member
From: Bahrain
Registered: 2006-01-11
Posts: 142

### Re: the area of the square and rectangle

can we talk in MSN ricky ?! i really feel that i am stupid ... yeah i know vectors ...

Last edited by RauLiTo (2006-07-22 08:32:08)

ImPo\$\$!BLe = NoTH!nG
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## #10 2006-07-22 12:11:35

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

### Re: the area of the square and rectangle

You want pictures?
Here:

Last edited by krassi_holmz (2006-07-22 12:13:27)

IPBLE:  Increasing Performance By Lowering Expectations.

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## #11 2006-07-22 23:11:32

RauLiTo
Member
From: Bahrain
Registered: 2006-01-11
Posts: 142

### Re: the area of the square and rectangle

PERFECT !!!
thank you very very much !!!

ImPo\$\$!BLe = NoTH!nG
Go DowN DeeP iNTo aNyTHinG U WiLL FinD MaTHeMaTiCs ...

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## #12 2006-07-22 23:34:53

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

### Re: the area of the square and rectangle

IPBLE:  Increasing Performance By Lowering Expectations.

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