Heron’s Formula: Area of a Triangle Knowing Lengths of 3 Sides: Algebraic Proof

▶️ Watch on 3Speak

---

In this video I take a break from my epic #AntiGravity Part 6 video which I have been working months on to instead go over a truly amazing formula for determining the Area of a Triangle with knowing only the lengths of the 3 sides. This famous formula is known as Heron’s Formula after the Greek Mathematician Hero (or Heron) of Alexandria as first documented in 60 AD. The formula is stated as such: The Area of a Triangle is the square root of s(s – a)(s – b)(s – c) where a, b, and c are the lengths of the 3 sides of a triangle, and s is the semiperimiter or half the perimeter of the triangle and is equal to (a + b + c)/2. Notice how this formula doesn’t require the height of the triangle or any angle in between the sides. I actually had never encountered this formula before, so I just had to make this video as soon as I learned of it! The derivation method that I used to prove the formula is by using an Algebraic method using the Pythagorean Theorem. Splitting the triangle into two smaller triangles by defining a height as the connecting side, I show that applying the Pythagorean Theorem twice and combined with a LOT of algebra, I can determine the height in terms of the lengths of the sides. Then plugging this height into the common Area = Base x Height / 2 formula, and some reformulation, we get the famous Heron’s Formula! Make sure to watch this video as it is a truly amazing example of how careful and tedious mathematics can eventually lead to a very simple and elegant final formula! #TrulyAmazingStuff

And now back to my researching for my #AntiGravity Part 6 video which is shaping up to be one of the most epic and important videos ever made in the history of what we like to call “reality”…. #STAYTUNED! #MyPhD

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIh6FcTkdHiZBee2LUsA

View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/heron-s-formula-area-of-a-triangle-knowing-lengths-of-3-sides-algebraic-proof

Related Videos:

Simple Proof of the Pythagorean Theorem:

Area of a Triangle - A simple proof that A = b*h/2:

Area of a Triangle Proof - Part 2: When the base is NOT the longest side of the triangle:

.

---

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Hive: https://peakd.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

---

▶️ 3Speak