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

Math Easy Solutions

First published at 08:02 UTC on May 16th, 2018.

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 Steemit: https://steemit.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: http://youtu.be/yt-EJlbJQp8
Area of a Triangle - A simple proof that A = b*h/2: http://youtu.be/wUT_KN5pshQ
Area of a Triangle Proof - Part 2: When the base is NOT the longest side of the triangle: http://youtu.be/xTVP-HHBP0U .


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