HERON'S FORMULA computing by meta007

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hive-196387 · @meta007 · Jun 14 '23 (edited)

$7.10

HERON'S FORMULA computing

Hello math bugs(🐞) and hivers(🐝)
I hope you are strong and stout & doing well in life.


Well come to another interesting geometric proof. We all know about Heron's formula used to find area of a triangle when three sides of it are given. I'll show you today how to drive it.

![](https://images.ecency.com/DQmP8RqR1sdZQwupxb2fEenQ7fJ2f5xGGtQ9kT1KHjBdjH5/addtext_06_09_04.39.23.png)

To prove it we need to know formula of **Pythagoras** and to do a little construction. At first, let's draw a perpendicular from a vertex to its opposite side of the ∆"*ABC**. Here I draw **AD** which os perpendicular to **BC**. Suppose, the three sides **a**, **b** , **c** are opposite to the respective angles **A**, angle **B** and angle **C** and also **BD**= x and **CD**= (a-x). Check details in the following figure:

![](https://images.ecency.com/DQmbCLqXqmEpMfVmGPAdfVRwL4WtAT2P72G4rNieQH9PHf9/addtext_06_12_10.17.40.png)

**Now we gonna use Pythagoras' formula in each of the smaller triangle namely** ∆**ABD** and ∆**ACD**. In case ∆ABD , we can say c² = x² + h² or h² = c² - x². Check the follwoing figure also:

![](https://images.ecency.com/DQmQmndncvnHZDKFKRYUE65AEtSQGUQcYvHTYV6s2FJ4ojk/addtext_06_12_10.42.24.jpg)

From ∆**ACD** , we also can get b² = (a-x)² + h² or h² = b² - a² -x² + 2ax. Check it below:


![](https://images.ecency.com/DQmQD1f1FmdKi9hNLcPLeb65xb3wQ5UVUZU8d7JNee8136q/addtext_06_14_08.02.45.jpg)

Check Heron's formula carefully. As there is no **x** or **h** in it. The the formula is given by **a**, **b** and **c** only. To get rid of **h** we need to compare equation1 and equation2  and we can have the value of **x**. Check the following figure:

![](https://images.ecency.com/DQmZ6iAD6GdM2Ee2xdATYbageyJ2BzAkqUuA8mJbi5wX7aT/addtext_06_14_08.47.32.jpg)


See, our moto is to get rid other variables except **a**, **b**, and **c**. What can we do now! If we replace the value of x in equation1 or 2, we will have an equation devoid of unwanted variables. As equation1 is simplier than equation2, we gonna use the former. Check the figure below:

![](https://images.ecency.com/DQmeMKUNKcDxxok7qoUaqyWvbsNbs9LeVbZxLcaBRomAx5W/addtext_06_14_10.13.59.png)

We know the area of a triangle is given by 1/2 ×base × height.  Here we have consider **a** as base and height **h**. Once we find vaule of **h** from above equation, problem is solved because the vaule of **h** we gonna obtained will be in terms of three sides( a,b & c) of the ∆ABC. let's get it done.


![](https://images.ecency.com/DQmUT89hpPAwNvXFRguvkaB7qRTRNEfo7wwGCuryHp8qrie/addtext_06_14_10.48.24.jpg)
Now area will be 1/2× base × height =1/2× a×√(S(S-a)(S-b)(S-c) unit². Also check the following figure:


![](https://images.ecency.com/DQmbn8u5nnckHmKgs82kaNFwvhbuWGV6jiZNkBBH9F7Fw2b/addtext_06_14_11.09.03.jpg)

**All the figures and images are made by me using android application.**

Please ignore the silly mistake(s) of there is any. All the figures you have seen take huge time to build. So re-editing hurts.

I hope you find this post interesting ans effortful. Thank you so much for visiting. 

Have a good day. 

All is well.

Regards: @meta007

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joseluis91	6,355,173,869	41%
miroslaviv	1,087,552,339	1.4%
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muterra	147,167,632,065	20%
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drhueso	638,240,537	1.4%
yoieuqudniram	2,018,786,592	20.5%
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aries90	20,626,779,447	2.8%
hyun-soo	870,723,327	17.5%
cugel	886,615,029	1.4%
iradeorum	538,851,195	100%
kraaaaa	628,101,653	3.12%
deimage	3,175,660,880	10%
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jude9	1,587,654,569	10%
castles	829,584,968	41%
yixn	26,214,968,390	1.4%
kqaosphreak	2,529,713,105	35%
alt3r	696,156,713	2.15%
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crimsonowl-art	642,080,491	20.5%
raph1	3,621,449,255	100%
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thgaming	1,303,258,990	6.25%
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dondido	10,373,996,863	2.8%
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baboz	584,640,609	0.7%
sbtofficial	2,114,007,535	1.4%
vagabond42069	732,505,851	17.5%
inibless	1,625,470,348	17.5%
cindynancy	636,007,471	17.5%
genepoolrentsclr	696,367,485	1.4%
carolinaes	652,391,512	20.5%
sc000	651,800,081	2.8%
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jijisaurart	533,296,633	1.4%
workaholic666	323,058,308	100%
minas-glory	1,733,718,832	1.4%
clpacksperiment	1,094,415,050	1.4%
the-grandmaster	1,797,948,276	1.4%
the-burn	1,801,022,168	1.4%
grindan	1,381,155,091	0.84%
abu78	2,255,234,967	12.25%
reverio	981,140,658	5%
arduilcelebren	511,281,280	1.4%
abhay2695	1,208,636,055	10%
lettinggotech	622,031,574	1.4%
bank-of-woo	12,166,462,236	25%

@discovery-it · Jun 15 '23

<div class="pull-left">https://cdn.steemitimages.com/DQmTAn3c753LR7bHCLPo96g9UvRMaPFwaMYn8VQZa85xczC/discovery_logo_colore%20-%20Copia.png</div><br> This post was shared and voted inside the discord by the curators team of <a href="https://discord.gg/cMMp943"> discovery-it</a> <br>Join our <a href = "https://hive.blog/trending/hive-193212"> Community</a> and follow our <a href = "https://hive.vote/dash.php?i=1&trail=discovery-it">Curation Trail</a><br>Discovery-it is also a Witness, vote for us <a href = "https://hivesigner.com/sign/account-witness-vote?witness=discovery-it&approve=true"> here</a>  <br>Delegate to us for passive income. Check our <a href = "https://hive.blog/hive-193212/@discovery-it/delegations-program-80-fee-back"> 80% fee-back Program</a> <hr>

👍 meta007

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@enforcer48 · Jun 15 '23

The tough part here is keeping track of all the variables. Gotta love math sometimes.

!discovery 41

👍 dustbunny, meta007
👎 stimialiti

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@meta007 · Jun 15 '23

$0.07

Yeah there are a lot of variables and all should be taking care of at the same time. Good to know that you love math sometimes. The same goes for me 😄😄.

Thanks man for visiting

👍 enforcer48, stemgeeks, yggdrasil.laguna

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@gabrielr29 · Jun 15 '23

I keep thinking of Galileo Galilei's phrase when mathematics is taught with passion: "Mathematics is the language with which God wrote the universe".

I love it when someone shares their knowledge with passion and fervor. I wish you much success. The images didn't load very well but it could be because of my internet, it is very deficient here.

👍 meta007, stemgeeks, yggdrasil.laguna

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@meta007 · Jun 15 '23

Yeah it's a wonder. It seems the universe is like a balanced equation of mathematics. 

As for image, it may be the app. issue.

Thanks man for encouraging and supporting.

👍 gabrielr29, stemgeeks, yggdrasil.laguna

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@hivebuzz · Jun 14 '23

Congratulations @meta007! You have completed the following achievement on the Hive blockchain And have been rewarded with New badge(s)

<table><tr><td><img src="https://images.hive.blog/60x70/http://hivebuzz.me/@meta007/posts.png?202306141117"></td><td>You published more than 50 posts.<br>Your next target is to reach 60 posts.</td></tr>
</table>

<sub>_You can view your badges on [your board](https://hivebuzz.me/@meta007) and compare yourself to others in the [Ranking](https://hivebuzz.me/ranking)_</sub>
<sub>_If you no longer want to receive notifications, reply to this comment with the word_ `STOP`</sub>


To support your work, I also upvoted your post!


**Check out our last posts:**
<table><tr><td><a href="/hive-122221/@hivebuzz/lpud-202306"><img src="https://images.hive.blog/64x128/https://i.imgur.com/pVZi2Md.png"></a></td><td><a href="/hive-122221/@hivebuzz/lpud-202306">LEO Power Up Day - June 15, 2023</a></td></tr></table>

👍 meta007

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@indiaunited · Jun 14 '23

Indiaunited Curation 1686766615146

This post has been manually curated by @bhattg from Indiaunited community. Join us on our [Discord Server](https://discord.gg/bGmS2tE). 

Do you know that you can earn a passive income by delegating to @indiaunited. We share more than 100 % of the curation rewards with the delegators in the form of IUC tokens. HP delegators and IUC token holders also get upto 20% additional vote weight. 

Here are some handy links for delegations: [100HP](https://hivesigner.com/sign/delegateVestingShares?delegator=&delegatee=indiaunited&vesting_shares=177329.8448160782%20VESTS), [250HP](https://hivesigner.com/sign/delegateVestingShares?delegator=&delegatee=indiaunited&vesting_shares=443324.61204019556%20VESTS), [500HP](https://hivesigner.com/sign/delegateVestingShares?delegator=&delegatee=indiaunited&vesting_shares=886649.2240803911%20VESTS), [1000HP](https://hivesigner.com/sign/delegateVestingShares?delegator=&delegatee=indiaunited&vesting_shares=1773298.4481607822%20VESTS). 

[![image.png](https://files.peakd.com/file/peakd-hive/bala41288/46eaz12N-image.png)](https://discord.gg/bGmS2tE) 

<sub>**100% of the rewards from this comment goes to the curator for their manual curation efforts. Please encourage the curator @bhattg by upvoting this comment and support the community by voting the posts made by @indiaunited.**</sub>

👍 meta007

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@stemsocial · Jun 15 '23

re-meta007-heron-s-formula-computing-20230615t032217864z

<div class='text-justify'> <div class='pull-left'>
 <img src='https://stem.openhive.network/images/stemsocialsupport7.png'> </div>

Thanks for your contribution to the <a href='/trending/hive-196387'>STEMsocial community</a>. Feel free to join us on <a href='https://discord.gg/9c7pKVD'>discord</a> to get to know the rest of us!

Please consider delegating to the @stemsocial account (85% of the curation rewards are returned).

Thanks for including @stemsocial as a beneficiary, which gives you stronger support.&nbsp;<br />&nbsp;<br />
</div>

👍 meta007

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