Triangle area proofs | Perimeter, area, and volume | Geometry | Khan Academy

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Proving that the area of any triangle is 1/2 b x h
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[@matthewsullivan2381]

This is great. A lot of people teaching math will be like "Area equals 1/2 times the base times the height", without explaining why. Much clearer this way, Thanks :)

[@ChocolaVanillarune2005]

This is so useful for my upcoming test I JUST HAVE TO PASS!!!! Thank you :)

[@aaronleperspicace1704]

In the second case, where the top vertex of the triangle (obtuse angled) lies "outside" of its base, (meaning that you'd end up throwing the rock outside the triangle if you threw it straight down the vertex), another way to do it , without adding a triangle would be to rotate the triangle so that the obtuse angle is overhead and dropping a rock actually lands it inside the triangle. This also illustrates that unless your triangle is an equilateral triangle, it does not have a single base or a single height, it all depends on which vertex you put at the top. The area remains the same, of course.

[@chancegamesone]

That angle is 90-x because the first angle (the one on the bottom left) is 90 degrees, and all three angles in a triangle will always add up to 180 degrees. If the angle on the right is x, the top angle must be 90-x in order for all three to add up to 180 degrees.

[@lina72]

My Daughter is having her SSATS this Saturday and this really helped her Thank You!!!

[@noobletify869]

Thank you for the video, it was very helpful. I am in year eleven and all those years I had never known exactly how 0.5bh could be used for a triangle such as the third one shown in the video. It was very nicely explained.

[@zecgallo2358]

Holy crap this will be our lesson tomorrow and I didn't notice that we we're already in geometry.

[@katyknyazko1267]

confusing but still got it, thanks!

[@regulareverydaynormalguy8789]

man this is great and thanks

[@dlgbeats]

It helped alot

[@vaccino3359]

I'd like to do a pro gamer move for the last triangle by duplicating and placing it over the triangle and flipping it so it makes a Parallelogram. The area of a parallelogram is Base * Altitude and since it is twice the triangle, 0.5 (base)(Altitude). 0.5 is 1/2.

[@saulfigueroa7510]

thanks for the lesson i got 10/10 on my test

[@sangamesh2727]

I was looking for the third one.

[@umamahobeidullah4022]

I learned in school that the area of a triangle exept the right angles is half times two sides times sin of included angle

[@chancedelagarrigue4971]

Thx for the help

[@iegend6371]

I understand it in first 4 Lin's of yours

[@tyreicehammonds9737]

This helped me a lot thanks

[@fredytay2122]

thanks

[@Arkay24]

Awesome :D

[@dlgbeats]

RogueKnight24 yass😂

[@MohamedGaber111]

Also nice

[@gray8374]

Be my teacher, please. You would be perfect.

[@ellaaldc4life]

My parents force me to watch this but it does teach me ty

[@badrakram3422]

o, and can you tell me how to make a video using khan academy, i really want to get the black hole badge

[@krishnakantsingh3548]

Area of rectangle is proved on area of triangle and area of triangle is proved on area of rectangle. AMAZING RELATION how could be it possible

[@johnsoutsideworld3454]

good vid

[@sammrguy03]

For the third one, couldn’t you rotate the triangle so that BA is the base? That way the proof from the second triangle applies.

[@ringoffire0]

Well, now you can do (1/2)*B*H using ANY side of the triangle as the base. Whether the case is, the third vertex is directly above another, in between the two vertices, or neither, the equation holds.

[@badrakram3422]

Nice

[@narsireddy7399]

i saw the explanation proof of triangle of yours .you do not beleive that you think same like me in finding the proof of triangle isaw the other derivation which was said by my brother

[@evoman3dfx]

it is a little confusing but i get it.

[@stepans2961]

help

[@stephankyng651]

Next time try explain wat triangle your using

[@-Ori_g-]

Ain't no way blud used area of a triangle to prove area of a triangle 💀😭 Area of a rectangle is based on area of a triangle.

[@saucymoses8582]

MORE MORE!

[@dlgbeats]

Derpy PvP hahahahahah yes more

[@saucymoses8582]

LOLOLOL

[@Oxcilic]

Why is that angle 90-x? please explain simply....

[@vlogtomejr.1919]

Hello! The triangle sum theorem states that the sum of all the angles in a triangle equal 180°.

[@jerfersonmatos28]

Every "RIGHT TRIANGLES" have a 90° angle. And a right triangle is when you have a vertical line "|", a horizontal line "_" , and a diagonal line "\". The 90° angle is between the vertical and horizontal lines

[@mr.jakir.rathore]

Oxcilic थतघ

[@marvhartigan3677]

Bro one of the angles is 90, assume one of the other angles is x, now since sum of abgles of a triangle is 180 degrees 90 degrees is already gone rem is x degrees and the other angle now since only 90 degree is left the other angle will be 90-x

[@ellaaldc4life]

i was born 20th april 2011...

[@amberbuechler3317]

who is meaner inosuke or bakugou

[@SB-fo7em]

7:03 can't we just rotate the triangle? it'd be a lot easier??

[@mathogenynavedahmad1635]

U proved this by using formula.proved 1/2 bxh.mathematician didn't prove by this method.what is the real method