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What is the name of following formula? $$ S=\sqrt[]{(p-a)(p-b)(p-c)(p-d)} $$ where $$ a+b+c+d=2p $$ $S$ is the surface of a quadrangle.

$a, b, c, d$ are lengths of sides of a quadrangle that can be inscribed into a circle.

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@Sawarnik In Italy I've always used $p$ for semi-perimeter and $s$ for surface. –  Bakuriu Mar 10 at 21:06
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@Bakuriu But everywhere I have seen uses $s$ as the semi-perimeter! Do you remember Heron s formula with $p$ as the semiperimeter? –  Sawarnik Mar 10 at 21:08
    
@Sawarnik Absolutely yes. Proof: wikipedia page on Heron's formula. –  Bakuriu Mar 10 at 21:10
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@Bakuriu That is really odd! But most of the world uses $s$, I think. English Wikipedia can be a proof for that. Oh, I see he is from Poland, and the Polish Wiki does use $p$! –  Sawarnik Mar 10 at 21:11

1 Answer 1

up vote 10 down vote accepted

Brahmagupta's formula. You can do a google search. Or here is the wikipedia link.

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Hmm...nice answer badge :) –  Sawarnik Mar 11 at 15:16
    
@Sawarnik yep :) –  Sabyasachi Mar 11 at 15:23
    
Interestingly I didn't know the name of this formula 10 mins before answering. The credit is due to another question. I get a silver badge and 115 rep for free. :D –  Sabyasachi Mar 11 at 15:24
    
I know..the pentagon question after mine, isn't it? It was a nice Q, its inspired me to read stuff about Robbins pentagon and so...but how come a 1 line answer get 10 upvotes, I am jealous of you..btw, reputation is a useless thing. –  Sawarnik Mar 11 at 15:51
    
@Sawarnik yep. The one after yours. It was weird though, two different people asking about pentagons in such a short while. Since when are cyclic pentagons the new trend? –  Sabyasachi Mar 11 at 16:05

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