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 2 years ago
Hey friends. This is not a question but a tutorial on Heron's formula .. please see the attachment
 2 years ago
Hey friends. This is not a question but a tutorial on Heron's formula .. please see the attachment

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mathslover
 2 years ago
Best ResponseYou've already chosen the best response.43any suggestions and feedbacks will be welcomed. ..

rebeccaskell94
 2 years ago
Best ResponseYou've already chosen the best response.2I can't get it to download right, sorry :c

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.43is their any problem with file or downloading speed is low @rebeccaskell94 ?

rebeccaskell94
 2 years ago
Best ResponseYou've already chosen the best response.2The file. Some files when I convert them/download them only upload as symbols and stuff.

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.43wait i am going to type that all soon

rebeccaskell94
 2 years ago
Best ResponseYou've already chosen the best response.2Okay :) Just tag me again and I'll come back. I must go study now c:

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0you made this maths?

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.43yes @lgbasallote ..

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.0one of the most useful formulas in geometry thank u @mathslover very useful tutorial

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.43gr8 to know @mukushla thanks a lot

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1why does herons formula work?

kritima
 2 years ago
Best ResponseYou've already chosen the best response.0great job mathslover ! i think it's going to help me a lot

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.43gr8 to know @kritima @UnkleRhaukus do u mean for proof

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.43it is very long .. can u just wait for some time i will upload soon

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.43i have got it upto very nearer ... for the proof

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.43HERONS' FORMULA : Basically Herons' formula is : Area of a triangle = \(\sqrt{s(sa)(sb)(sc)}\) where s =\(\frac{a+b+c}{2}\) and a , b and c are the sides of a triangle s can also be said as : semi perimeter as a + b + c = perimeter of a triangle and when we half it ..then it becomes semi perimeter . I should also introduce you all with : a basic formula for the triangle area : (base*corresponding height) / 2 In some cases we are not able to find the height .. but we are given with all sides of the triangle.. Hence in that case we generally use : heron's formula to find the area of a triangle For example : Find the area of a triangle having sides : 5 cm , 6 cm and 10 cm . In this case we are unable to find the height .. Hence we will be going to use : herons' formula \[\large{s=\frac{5 cm + 6 cm + 10 cm}{2}=\frac{21 cm }{2}}\] now applying the formula : area of the triangle : \(\sqrt{\frac{21}{2}(\frac{21}{2}5)(\frac{21}{2}6)(\frac{21}{2}10)}\) \[\large{\sqrt{\frac {21}{2}*\frac{11}{2}*\frac{9}{2}*\frac{1}{2}}}\] \[\large{\sqrt{\frac{21*11*9*1}{2^4}}}\] \[\large{\sqrt{\frac{21*11*3^2*1^2}{(2^2)^2}}}\] \[\large{\frac{3}{4}\sqrt{231}}\] hence the area of the triangle with the given information will be \(\frac{3}{4}\sqrt{231}\) Now coming to the main point : area of an equilateral triangle : (base*corresponding height)/2 Since this is an equilateral triangle : having all sides equal ( let it be : a ) \[\large{\frac{a*h}{2}}\] Now we will calculate h ( height ) as we know that whenever we draw a perpendicual bisector on a base of an equilateral triangle , it will divide the base into 2 equal parts . hence the equal divided lengths of the base = \(\frac{a}{2}\) as per pythagoras theorem : \[\large{h^2+\frac{a^2}{4}=a^2}\] \[\large{h^2=a^2\frac{a^2}{4}}\] \[\large{h^2=\frac{3a^2}{4}}\] \[\large{h=\sqrt{\frac{3a^2}{4}}}\] \[\large{h=\frac{\sqrt{3}}{2}a}\] \[\large{h=\frac{\sqrt{3}a}{2}}\] \[\large{\textbf{Area of the equilateral triangle}=\frac{a*h}{2}}\] \[\large{\textbf{Area of the equilateral triangle}=\frac{a*\frac{\sqrt{3}a}{2}}{2}}\] \[\large{\textbf{Area of the equilateral triangle}=\frac{\sqrt{3}a^2}{4}}\] Now prooving this formula by heron's formula \[\sqrt{s(sa)(sb)(sc)}=\textbf{Area of the equilateral triangle}\] \[\sqrt{\frac{3a}{2}(\frac{3a}{2}a)(\frac{3a}{2}a)(\frac{3a}{2}a)}\] \[\sqrt{\frac{3a}{2}*\frac{a}{2}*\frac{a}{2}*\frac{a}{2}}\] \[\sqrt{\frac{3a^4}{2^4}}\] \[\frac{a^2}{4}\sqrt{3}\]

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.43@estudier @Diyadiya @annas @rebeccaskell94 @Romero @satellite73 @ujjwal

rebeccaskell94
 2 years ago
Best ResponseYou've already chosen the best response.2You really wrote this?

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.43yes ..r u talking about that pdf file or this. . latex file ?

rebeccaskell94
 2 years ago
Best ResponseYou've already chosen the best response.2This Latex one. Your English is really good for this, so I was kinda surprised! Good job :)

annas
 2 years ago
Best ResponseYou've already chosen the best response.1awesome @mathslover your work is clearly appreciable ... keep up the good work and god bless you bro!!

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.43thanks a lot annas ... just needed all of ur's wishes . . . that is what i got ! thanks a lot I promise that i will continue to maintain this ...

annas
 2 years ago
Best ResponseYou've already chosen the best response.1@rebeccaskell94 you can download it by pressing right mouse button a box will appear with some options there is an option save as click it ... file will be downloaded as .pdf

rebeccaskell94
 2 years ago
Best ResponseYou've already chosen the best response.2Well it has that, but sometimes it downloads weird. It's not really a big deal, it's just frustrating.

annas
 2 years ago
Best ResponseYou've already chosen the best response.1sometimes your system cant identify some symbols because there ASCII codes are unknown to CPU ... btw .pdf files never create problems

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.43@lalaly @jiteshmeghwal9 @TheViper @maheshmeghwal9 @ash2326 @goformit100 @robtobey @waterineyes @CarlosGP

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.43@amistre64 sir please have a look

jiteshmeghwal9
 2 years ago
Best ResponseYou've already chosen the best response.1nice work:) latex one is a very very nice one :D

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.43thanks @jiteshmeghwal9 that's why i put up latex here also .... in the place of that pdf ..so that all can view easily ...

jiteshmeghwal9
 2 years ago
Best ResponseYou've already chosen the best response.1yeah it is really better.

jiteshmeghwal9
 2 years ago
Best ResponseYou've already chosen the best response.1& i think the best.

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.43thanks @jiteshmeghwal9 ...more comments and suggestions will be appreciated and welcomed

Libniz
 2 years ago
Best ResponseYou've already chosen the best response.0draw more picture , less words

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.43So here i go with the explanation for : \[\textbf{How to find the area of a quadrilateral using heron's formula}\] dw:1342456404056:dw In the above diagram we have : a quadrilateral .. So how to find the area of a quadrilateral ..having sides a , b , c and d as i drew the diagonals of the quadrilateral .. we can find the area of the quadrilateral very easily .. let me show u all how .

lalaly
 2 years ago
Best ResponseYou've already chosen the best response.0Amazing:D thanks for sharing @mathslover

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.43dw:1342456608856:dwdw:1342456626544:dw

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.43So from this we have 2 triangles : ACD and ABC now : \(Ar(ACD)+Ar(ABC)=Ar(ABCD)\) hence first calculating \(Ar(ACD)\) as we know that the area of a triangle = \(\large{\frac{b*h}{2}}\) hence \[\large{Ar(ACD)=\frac{c*h_1}{2}}\] and similarly \(Ar(ABC)\) : \[\large{Ar(ABC)=\frac{a*h_2}{2}}\] hence now adding them we get : \[\large{Ar(ABCD)=\frac{c*h_1}{2}+\frac{a*h_2}{2}}\] \[\large{Ar(ABCD)=\frac{(c*h_1)+(a*h_2)}{2}}\]

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.43We can calculate this also by using heron's formula : Let the diagonal be x : hence : 1) \(Ar(ACD)=\sqrt{\frac{(a+c+d)}{2}(a+c+dd)(a+c+dc)(a+c+da)}\) \(Ar(ACD)=\sqrt{\frac{(a+c+d)}{2}(a+c)(a+d)(c+d)}\) 2) \(Ar(ABC)=\sqrt{\frac{(a+b+x)}{2}(a+b+xa)(a+b+xx)(a+bb+x)}\) \(Ar(ABC)=\sqrt{\frac{(a+b+x)}{2}(b+x)(a+b)(a+x)}\) finally adding both these equations we may get the area of the quadrilateral .. This seems hard but one if we get the values of the sides then we can calculate this very easily .. I am going to explain this to you all by taking an example : Find the area of a quadrilateral having sides : a = 4 cm. b = 3 cm. c = 10 cm. d = 12 cm. diagonal ( x ) = 5 cm. dw:1342457755184:dw

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.43given x = 5 cm .. Hence we have all sides in 1st part of the triangle : calculating the area of the first part of the quadrilateral : 1) \(Ar(fig.1)=\sqrt{6(2)(3)(1)cm^4}\) \(Ar(fig.1)=6 cm^2\) 2) \(Ar(fig.2)=\sqrt{\frac{27}{2}*\frac{7}{2}*\frac{3}{2}*\frac{17}{2}}\) \(Ar(fig.2)=\sqrt{\frac{9*9*17*7}{2^4}}\) \(Ar(fig.2)=\frac{9}{4}\sqrt{119}\) Hence adding them we get : \[Ar(Quadrilateral)=6 cm^2+\frac{9}{4}\sqrt{119} cm^2\]

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.43Hope it helps .. thats all thanks mathslover

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1342458885083:dw

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.0r'_a is a radius of External surrounded circle and r related to inner circle.

mahmit2012
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1342459347799:dw

Hero
 2 years ago
Best ResponseYou've already chosen the best response.0Would have been a great video tutorial if the feature existed.

Vaidehi09
 2 years ago
Best ResponseYou've already chosen the best response.0great job @mathslover. its quite detailed with explanations for each step. plus the examples! i'd say job well done!

maheshmeghwal9
 2 years ago
Best ResponseYou've already chosen the best response.0nice work!!!!! well that's the tutorial i would love to say:D

sami21
 2 years ago
Best ResponseYou've already chosen the best response.0nice ineresting..u did all of this . awsum.

kropot72
 2 years ago
Best ResponseYou've already chosen the best response.0A very interesting topic. This formula goes way back in history. Thanks for your good work mathslover.

Ron.mystery
 2 years ago
Best ResponseYou've already chosen the best response.0got the medal dude!! but nice work as better as LGBA and he's the best on this so a fab job is been done!! @mathslover

cwrw238
 2 years ago
Best ResponseYou've already chosen the best response.0brilliant work!!  your name is appropriate mathslover

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.43gr8 to know thanks a lot @Ron.mystery and @cwrw238 .... I hope this will be useful for all @estudier

Calcmathlete
 2 years ago
Best ResponseYou've already chosen the best response.0Great job! Heron's formula really can be very useful. It's a bit unfortunate you usually don't learn it until higher levels of math though...Nevertheless, awesome work :)

anjali_pant
 2 years ago
Best ResponseYou've already chosen the best response.0nice tutorial ! Great work @mathslover ! :)

Master.RohanChakraborty
 2 years ago
Best ResponseYou've already chosen the best response.0good job my bro!! love u!!

across
 2 years ago
Best ResponseYou've already chosen the best response.0Thanks for referring me to this. I'll give it a look later.

sami21
 2 years ago
Best ResponseYou've already chosen the best response.0i think so this is a record!

Hero
 2 years ago
Best ResponseYou've already chosen the best response.0Hey everybody, go back to my post, lol

jiteshmeghwal9
 2 years ago
Best ResponseYou've already chosen the best response.1\[\Huge{\color{gold}{\star \star \star}\color{red}{breacked \space the \space record \space of \space lgbasallote}}\]

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0FINALLY! SOMEONE BEATS MY RECORD!! i can peacefully retire form tutorials now ^_^

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.43@RahulZ @rajathsbhat

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.43@RahulZ please comment

RahulZ
 2 years ago
Best ResponseYou've already chosen the best response.0Hey u made the tutorial , it was cool ,.... really cool

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.43Nice to hear. .. . .. well u in which class ?

RahulZ
 2 years ago
Best ResponseYou've already chosen the best response.0I am an University student. :)
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