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

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mathsloverBest ResponseYou've already chosen the best response.43
any suggestions and feedbacks will be welcomed. ..
 one year ago

rebeccaskell94Best ResponseYou've already chosen the best response.2
I can't get it to download right, sorry :c
 one year ago

mathsloverBest ResponseYou've already chosen the best response.43
is their any problem with file or downloading speed is low @rebeccaskell94 ?
 one year ago

rebeccaskell94Best ResponseYou've already chosen the best response.2
The file. Some files when I convert them/download them only upload as symbols and stuff.
 one year ago

mathsloverBest ResponseYou've already chosen the best response.43
wait i am going to type that all soon
 one year ago

rebeccaskell94Best ResponseYou've already chosen the best response.2
Okay :) Just tag me again and I'll come back. I must go study now c:
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
you made this maths?
 one year ago

mathsloverBest ResponseYou've already chosen the best response.43
yes @lgbasallote ..
 one year ago

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

mathsloverBest ResponseYou've already chosen the best response.43
gr8 to know @mukushla thanks a lot
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.1
why does herons formula work?
 one year ago

kritimaBest ResponseYou've already chosen the best response.0
great job mathslover ! i think it's going to help me a lot
 one year ago

mathsloverBest ResponseYou've already chosen the best response.43
gr8 to know @kritima @UnkleRhaukus do u mean for proof
 one year ago

mathsloverBest ResponseYou've already chosen the best response.43
it is very long .. can u just wait for some time i will upload soon
 one year ago

mathsloverBest ResponseYou've already chosen the best response.43
i have got it upto very nearer ... for the proof
 one year ago

mathsloverBest ResponseYou've already chosen the best response.43
HERONS' 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 \[\sqrt{s(sa)(sb)(sc)}=\textbf{Area of the equilateral triangle}\] \[\sqrt{\frac{3a}{2}(\frac{3a}{2}a)(\frac{3a}{2}a)(\frac{3a}{2}a)}\] \[\sqrt{\frac{3a}{2}*\frac{a}{2}*\frac{a}{2}*\frac{a}{2}}\] \[\sqrt{\frac{3a^4}{2^4}}\] \[\frac{a^2}{4}\sqrt{3}\]
 one year ago

mathsloverBest ResponseYou've already chosen the best response.43
@estudier @Diyadiya @annas @rebeccaskell94 @Romero @satellite73 @ujjwal
 one year ago

rebeccaskell94Best ResponseYou've already chosen the best response.2
You really wrote this?
 one year ago

mathsloverBest ResponseYou've already chosen the best response.43
yes ..r u talking about that pdf file or this. . latex file ?
 one year ago

rebeccaskell94Best ResponseYou've already chosen the best response.2
This Latex one. Your English is really good for this, so I was kinda surprised! Good job :)
 one year ago

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

mathsloverBest ResponseYou've already chosen the best response.43
thanks 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 ...
 one year ago

annasBest 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
 one year ago

rebeccaskell94Best ResponseYou've already chosen the best response.2
Well it has that, but sometimes it downloads weird. It's not really a big deal, it's just frustrating.
 one year ago

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

mathsloverBest ResponseYou've already chosen the best response.43
@lalaly @jiteshmeghwal9 @TheViper @maheshmeghwal9 @ash2326 @goformit100 @robtobey @waterineyes @CarlosGP
 one year ago

mathsloverBest ResponseYou've already chosen the best response.43
@amistre64 sir please have a look
 one year ago

jiteshmeghwal9Best ResponseYou've already chosen the best response.1
nice work:) latex one is a very very nice one :D
 one year ago

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

jiteshmeghwal9Best ResponseYou've already chosen the best response.1
yeah it is really better.
 one year ago

jiteshmeghwal9Best ResponseYou've already chosen the best response.1
& i think the best.
 one year ago

mathsloverBest ResponseYou've already chosen the best response.43
thanks @jiteshmeghwal9 ...more comments and suggestions will be appreciated and welcomed
 one year ago

LibnizBest ResponseYou've already chosen the best response.0
draw more picture , less words
 one year ago

goformit100Best ResponseYou've already chosen the best response.0
Thanks @mathslover
 one year ago

mathsloverBest ResponseYou've already chosen the best response.43
So 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 .
 one year ago

lalalyBest ResponseYou've already chosen the best response.0
Amazing:D thanks for sharing @mathslover
 one year ago

mathsloverBest ResponseYou've already chosen the best response.43
dw:1342456608856:dwdw:1342456626544:dw
 one year ago

mathsloverBest ResponseYou've already chosen the best response.43
So 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 : \[\large{Ar(ABCD)=\frac{c*h_1}{2}+\frac{a*h_2}{2}}\] \[\large{Ar(ABCD)=\frac{(c*h_1)+(a*h_2)}{2}}\]
 one year ago

mathsloverBest ResponseYou've already chosen the best response.43
We 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
 one year ago

mathsloverBest ResponseYou've already chosen the best response.43
given 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 : \[Ar(Quadrilateral)=6 cm^2+\frac{9}{4}\sqrt{119} cm^2\]
 one year ago

mathsloverBest ResponseYou've already chosen the best response.43
Hope it helps .. thats all thanks mathslover
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.0
dw:1342458885083:dw
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.0
r'_a is a radius of External surrounded circle and r related to inner circle.
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.0
dw:1342459347799:dw
 one year ago

HeroBest ResponseYou've already chosen the best response.0
Would have been a great video tutorial if the feature existed.
 one year ago

Vaidehi09Best ResponseYou've already chosen the best response.0
great job @mathslover. its quite detailed with explanations for each step. plus the examples! i'd say job well done!
 one year ago

maheshmeghwal9Best ResponseYou've already chosen the best response.0
nice work!!!!! well that's the tutorial i would love to say:D
 one year ago

sami21Best ResponseYou've already chosen the best response.0
nice ineresting..u did all of this . awsum.
 one year ago

kropot72Best ResponseYou've already chosen the best response.0
A very interesting topic. This formula goes way back in history. Thanks for your good work mathslover.
 one year ago

Ron.mysteryBest ResponseYou've already chosen the best response.0
got 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
 one year ago

cwrw238Best ResponseYou've already chosen the best response.0
brilliant work!!  your name is appropriate mathslover
 one year ago

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

CalcmathleteBest ResponseYou've already chosen the best response.0
Great 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 :)
 one year ago

anjali_pantBest ResponseYou've already chosen the best response.0
nice tutorial ! Great work @mathslover ! :)
 one year ago

Master.RohanChakrabortyBest ResponseYou've already chosen the best response.0
good job my bro!! love u!!
 one year ago

acrossBest ResponseYou've already chosen the best response.0
Thanks for referring me to this. I'll give it a look later.
 one year ago

sami21Best ResponseYou've already chosen the best response.0
i think so this is a record!
 one year ago

HeroBest ResponseYou've already chosen the best response.0
Hey everybody, go back to my post, lol
 one year ago

jiteshmeghwal9Best ResponseYou've already chosen the best response.1
\[\Huge{\color{gold}{\star \star \star}\color{red}{breacked \space the \space record \space of \space lgbasallote}}\]
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
FINALLY! SOMEONE BEATS MY RECORD!! i can peacefully retire form tutorials now ^_^
 one year ago

mathsloverBest ResponseYou've already chosen the best response.43
@RahulZ @rajathsbhat
 one year ago

mathsloverBest ResponseYou've already chosen the best response.43
@RahulZ please comment
 one year ago

RahulZBest ResponseYou've already chosen the best response.0
Hey u made the tutorial , it was cool ,.... really cool
 one year ago

mathsloverBest ResponseYou've already chosen the best response.43
Nice to hear. .. . .. well u in which class ?
 one year ago

RahulZBest ResponseYou've already chosen the best response.0
I am an University student. :)
 one year ago
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