Part 1 of proof of Heron's formula | Perimeter, area, and volume | Geometry | Khan Academy

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Part 1 of the proof of Heron's Formula

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Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

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I love how I could pretty much prove this on my own before I even watched this video. Yet a few moths ago a I barely passed my test by 1%
. Somehow khan academy has boosted me beyond ever actually needing to watch the videos. Like I find everything so easy in class now having it explained to me twice is useless. Thanks Khan, I love math!

griftorifto
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Well, as of today, I don't get Heron's proof of formula here and I know with time, eventually, I will comprehend. Khan Academy is wonderful and I'll be back to share my transformation on this particular proof.

Monique_Johnson
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Thank you you simplified the last step! :D

mashupstyles
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It is so entertaining, I'm hooked ;) and of course informative and I loved it. If you don't mind telling me, what pad are you using to draw? It looks like it has no lag. cheers and thanks for the video, it is a good brain exercise too ;)

lashamamaladze
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Which software you use for making videos?

TheMusicalTech
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Please provide a link to the calculator application?

MaryDeioma
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How to download the calculator you used ?👌

kushshrivastava
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I am glad that height is discovered. When we will mutiply it with the base we will definitely get the area of the triangle. In case of 1' 2 and 3 first we may find the height of that particular triangle. In case we don' t got it then there the problem of discivoring height would be remain a mystery.

ahmedbaig
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I know; the "triangle" has an area of 0.

simonshugar
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Phillip wow u made a careless mistake a triangle cannot have sides 1, 2, 3 based on triangle inequality that would just make a line

ahmedattaalla
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Youtube won't let me type the up arrow so just imagine that the ampersand: & represents the power symbol.

(c - x) & 2=
(c - x) * (c - x) =
c * (c - x) - x * (c - x) =
c&2 - cx - cx + x&2 =
c&2 - 2cx + x&2

Also, if it was (c + x) & 2, the answer would be c&2 +2cx + x&2, notice that it is 2cx is not negative now. Most people have this memorized, that's why he didn't bother to explain it.

redjr
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@turquoiseguy Pythagoras theorem(s) to get step before that. Then multiplied it out and moved formula around

griftorifto
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Try to count how many times he says "squared" in this video.

deadlyvirtues
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The triangle obviously has an area of 0. The formula says that the area of the triangle is 1.11803398875...

simonshugar
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I have loaded few videos of area of Triangle, Herons Formula.

ahmedbaig
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You just did the math wrong. With a=1, b=2, c=3, the formula gives an area of zero as expected.

neoproletar
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This formula is not right. If you have side lengths 1, 2, and 3 on a triangle, it will have no area. Sides 1 and 2 put together = 3. I used the formula that you ended with for this video and substituted these numbers for the letters. a = 1, b = 2, and c = 3. The area of my "triangle" turned out being 1.11803398875... I did it on a calculator.

simonshugar
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Why kids love cinnamon toast crunch? Why kids like apple jacks when they don't taste like apples?

Slothd
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im doing a directed investigation on this and i am in yr 11 (16 yrs old)

bingflop
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is there anything this guy doesn't know?

bradq