mathslover
  • mathslover
Hey friends. This is not a question but a tutorial on Heron's formula .. please see the attachment
Mathematics
schrodinger
  • schrodinger
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mathslover
  • mathslover
mathslover
  • mathslover
any suggestions and feedbacks will be welcomed. ..
anonymous
  • anonymous
I can't get it to download right, sorry :c

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mathslover
  • mathslover
is their any problem with file or downloading speed is low @rebeccaskell94 ?
anonymous
  • anonymous
The file. Some files when I convert them/download them only upload as symbols and stuff.
mathslover
  • mathslover
wait i am going to type that all soon
anonymous
  • anonymous
Okay :) Just tag me again and I'll come back. I must go study now c:
lgbasallote
  • lgbasallote
you made this maths?
lgbasallote
  • lgbasallote
interesting
mathslover
  • mathslover
anonymous
  • anonymous
one of the most useful formulas in geometry thank u @mathslover very useful tutorial
mathslover
  • mathslover
gr8 to know @mukushla thanks a lot
UnkleRhaukus
  • UnkleRhaukus
why does herons formula work?
anonymous
  • anonymous
great job mathslover ! i think it's going to help me a lot
mathslover
  • mathslover
gr8 to know @kritima @UnkleRhaukus do u mean for proof
UnkleRhaukus
  • UnkleRhaukus
yeah,
mathslover
  • mathslover
it is very long .. can u just wait for some time i will upload soon
mathslover
  • mathslover
i have got it upto very nearer ... for the proof
mathslover
  • mathslover
HERONS' FORMULA : Basically Herons' formula is : Area of a triangle = \(\sqrt{s(s-a)(s-b)(s-c)}\) 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 \[\sqrt{s(s-a)(s-b)(s-c)}=\textbf{Area of the equilateral triangle}\] \[\sqrt{\frac{3a}{2}(\frac{3a}{2}-a)(\frac{3a}{2}-a)(\frac{3a}{2}-a)}\] \[\sqrt{\frac{3a}{2}*\frac{a}{2}*\frac{a}{2}*\frac{a}{2}}\] \[\sqrt{\frac{3a^4}{2^4}}\] \[\frac{a^2}{4}\sqrt{3}\]
mathslover
  • mathslover
anonymous
  • anonymous
You really wrote this?
mathslover
  • mathslover
yes ..r u talking about that pdf file or this. . latex file ?
anonymous
  • anonymous
This Latex one. Your English is really good for this, so I was kinda surprised! Good job :)
mathslover
  • mathslover
thanks
anonymous
  • anonymous
awesome @mathslover your work is clearly appreciable ... keep up the good work and god bless you bro!!
mathslover
  • mathslover
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 ...
anonymous
  • anonymous
@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
anonymous
  • anonymous
Well it has that, but sometimes it downloads weird. It's not really a big deal, it's just frustrating.
anonymous
  • anonymous
sometimes your system cant identify some symbols because there ASCII codes are unknown to CPU ... btw .pdf files never create problems
mathslover
  • mathslover
@amistre64 sir please have a look
jiteshmeghwal9
  • jiteshmeghwal9
nice work:) latex one is a very very nice one :D
mathslover
  • mathslover
thanks @jiteshmeghwal9 that's why i put up latex here also .... in the place of that pdf ..so that all can view easily ...
jiteshmeghwal9
  • jiteshmeghwal9
yeah it is really better.
jiteshmeghwal9
  • jiteshmeghwal9
& i think the best.
mathslover
  • mathslover
thanks @jiteshmeghwal9 ...more comments and suggestions will be appreciated and welcomed
anonymous
  • anonymous
draw more picture , less words
goformit100
  • goformit100
mathslover
  • mathslover
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 .
lalaly
  • lalaly
Amazing:D thanks for sharing @mathslover
mathslover
  • mathslover
|dw:1342456608856:dw||dw:1342456626544:dw|
mathslover
  • mathslover
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 : \[\large{Ar(ABCD)=\frac{c*h_1}{2}+\frac{a*h_2}{2}}\] \[\large{Ar(ABCD)=\frac{(c*h_1)+(a*h_2)}{2}}\]
mathslover
  • mathslover
We can calculate this also by using heron's formula : Let the diagonal be x : hence : 1) \(Ar(ACD)=\sqrt{\frac{(a+c+d)}{2}(a+c+d-d)(a+c+d-c)(a+c+d-a)}\) \(Ar(ACD)=\sqrt{\frac{(a+c+d)}{2}(a+c)(a+d)(c+d)}\) 2) \(Ar(ABC)=\sqrt{\frac{(a+b+x)}{2}(a+b+x-a)(a+b+x-x)(a+b-b+x)}\) \(Ar(ABC)=\sqrt{\frac{(a+b+x)}{2}(b+x)(a+b)(a+x)}\) 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
  • mathslover
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 : \[Ar(Quadrilateral)=6 cm^2+\frac{9}{4}\sqrt{119} cm^2\]
mathslover
  • mathslover
Hope it helps .. thats all thanks mathslover
hba
  • hba
yes ml
anonymous
  • anonymous
|dw:1342458885083:dw|
anonymous
  • anonymous
r'_a is a radius of External surrounded circle and r related to inner circle.
anonymous
  • anonymous
|dw:1342459347799:dw|
Hero
  • Hero
Would have been a great video tutorial if the feature existed.
anonymous
  • anonymous
great job @mathslover. its quite detailed with explanations for each step. plus the examples! i'd say job well done!
maheshmeghwal9
  • maheshmeghwal9
nice work!!!!! well that's the tutorial i would love to say:D
maheshmeghwal9
  • maheshmeghwal9
u deservedxD
anonymous
  • anonymous
nice ineresting..u did all of this . awsum.
kropot72
  • kropot72
A very interesting topic. This formula goes way back in history. Thanks for your good work mathslover.
anonymous
  • anonymous
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
cwrw238
  • cwrw238
brilliant work!! - your name is appropriate mathslover
mathslover
  • mathslover
gr8 to know thanks a lot @Ron.mystery and @cwrw238 .... I hope this will be useful for all @estudier
anonymous
  • anonymous
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 :)
anonymous
  • anonymous
nice tutorial ! Great work @mathslover ! :-)
anonymous
  • anonymous
good job my bro!! love u!!
across
  • across
Thanks for referring me to this. I'll give it a look later.
Hero
  • Hero
Record number of medals?
anonymous
  • anonymous
i think so this is a record!
Hero
  • Hero
Hey everybody, go back to my post, lol
jiteshmeghwal9
  • jiteshmeghwal9
\[\Huge{\color{gold}{\star \star \star}\color{red}{breacked \space the \space record \space of \space lgbasallote}}\]
lgbasallote
  • lgbasallote
FINALLY! SOMEONE BEATS MY RECORD!! i can peacefully retire form tutorials now ^_^
mathslover
  • mathslover
mathslover
  • mathslover
@RahulZ please comment
anonymous
  • anonymous
Hey u made the tutorial , it was cool ,.... really cool
anonymous
  • anonymous
i am taking a printout
mathslover
  • mathslover
Nice to hear. .. . .. well u in which class ?
anonymous
  • anonymous
I am an University student. :)
mathslover
  • mathslover
Oh !! nice.
mathslover
  • mathslover
mathslover
  • mathslover
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mathslover
  • mathslover

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