Area of a regular hexagon | Right triangles and trigonometry | Geometry | Khan Academy

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Using what we know about triangles to find the area of a regular hexagon
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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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[@MissMeganMarie99]

isnt it sad that I can get a better education off of youtube than in my high school math class! Thanks!

[@mauriciobeltre14]

Are you paying attention?

[@bgmarshall]

@@mauriciobeltre14 when you comment this the comment was atleast 3 years and 7 months old. Do they even remember that they commented this?

[@sheetal9257]

@@mauriciobeltre14 😂😂😂

[@willkershisnik5893]

@@mauriciobeltre14 this is an ignorant response to his statement

[@dy6mix]

@@bgmarshall7 years

[@nodariel]

I really love how maths can prove itself no matter what problem is involved. Great video :)

[@ivanwarrior2615]

Thx you helped with my homework when I watched your vids I'm in a 3rd grade class G.A.P class in Mr. Gordon

[@baranrafipour9362]

Woah you’re in 7th grade now, right?

[@sunitarawat9012]

You are in 8th now!

[@tamerali2099]

@@sunitarawat9012Lamo

[@TheNicholsjj]

A formula I came up with is when side length is SL you can then take 3SL* (SL/2)*sqrt3. It will always work.

[@triggerguard1]

The instruction is very well laid out, but it would be nice for you to use real numbers, as opposed to the square root of a number. I'm teaching math to a group of fabricators and I've done so with machinist, but the hypothetical numbers that are used in these examples are never applied in real-world environments. Angles aren't theta and sides aren't the square root of a number. Most of my students have had the misfortune of learning math in high school with this same logic, leaving them completely unaware of how to use it in the real world.

[@nikstopics5879]

GrizzlyMtn i

[@zack_120]

4:51 - at perpendicular conjunctions of two straight lines, only ONE 90 degree symbol is needed. The other side is automatically 90 degree based on 90+90=180: succinctness is the essence and beauty of math at least for this level (enjoyed this series!).

[@sillybunzy2839]

Thanks for the info!

[@ShakkIsLife]

The area of a regular hexagon is: (perimeter)(apothem)*1/2, where the apothem is the altitude of equilateral triangle.

[@alisabri2237]

We could have also used Heron's Formula to find the a area of a single triangle.

[@iluvbigbootie]

the long cut of finding the area shouldve use formula area= 1/2apothem*perimeter; with apothem= s/2*sqrt3. less chances for error.

[@thedarklight6752]

people who need only the apothem go to 3:00

[@corriynelise1032]

thanks

[@saraa1214]

Thx bro

[@javkhlanenkhbaatar3843]

saved my life.

[@Karurosuki]

I love how he is just like, "AND WERE DONE!" at the end. he might have not liked this lesson...

[@alibenaissabenaissa2463]

Thanks you helped me alot with my homework

[@T1mothy187]

Thank you!!

[@h0op2]

Thank you so much.

[@themusicmaster9241]

If anyone didnt understand 5:40 then watch "30-60-90 THEOREM BY KHAN ACADeMY" u will understand it

[@amrmukhtar8951]

Or use the Pythagorean theorem.

[@SubscribersNoVids-lu1rg]

If you're confused about the square roots numberings the adjacent side (small side)=x hypotenuse (large side)=2x opposite side (medium side)=X times the square root of 3

[@normavillado6980]

You help so much

[@rsimister]

lol at people quoting formulae. This is practice for logically breaking down problems, a skill you will need when formulae become inconvenient/nonexistent.

[@DevLuckk]

Great video who agrees

[@fazerisso]

Very good.

[@mohmoh-mp7es]

area of hexagon is 3.√3/2.a²

[@69faa69]

area of equal triangle= X^2*sqrt3 /4

[@sohamhalbandge8489]

thnxs

[@MrTigerman08]

hi, can you please remake the videos of calculus, and give some new examples.

[@humanbeeing4780]

Anybody here in 2021?

[@69faa69]

area of a hexagon 1.5*X^2*sqrt3 X=side

[@monjurahmed.]

Thanks

[@amjadmirza2343]

tht 3 concept u wrng u took the wrong side of it ,u have to take the side opposite ti the right angle nt the side whr the right angle is present

[@2kbling]

@khanacademy shouldn't it be multiplied by 12 since the right triangle is half the equilateral triangle

[@abhijeetbhatta9017]

Cant we just use the formula for equalateral triangle instead????.that way we don't have to figure out the height

[@deanna.111]

We're learning about this and I'm in 7th grade 😩 I'm not even in honors or accelerated

[@banothraju8276]

with 5 areas out of six, of six pointed star are given, how to find out the sixth area of the triangle with thoose given 5 areas ? anyone pls help me.

[@user-vs1lm6fy3x]

IDK if its just sleep deprivation but I'm still confused

[@rounaksharma3672]

this doesn't apply on every no. like try on 6cm of each side of hexagon... try this-3√3 a^2/2

[@keenansmith6163]

What does he mean by "Two squareds of 3". How what does that equation mean and how can I read it?

[@keenansmith6163]

Is 2√3 = 3.4641016151377545870548926830117

[@ZDrive]

What program did you use to make the marks in this video?

[@starbreaker8513]

I'm, what happened to splitting the hexagon into 2 trapezoids?...

[@eyelashbug5461]

if i know one side do i do that number multiplied by six?

[@boxhead8694]

No 2kbling, he found the area of 1 triangle then multiplied by 6. Your referring to HALF A TRIANGLE!

[@Anonymous-bq9df]

Nope. He changed it later..and found the area of the whole triangle.

[@Krishnam-g2u]

Cyblohexane

[@Jessica-kq5pg]

I still don't understand it

[@zoeparker3847]

III • it’s always 6 equilateral triangles so you can just use the equilateral triangle area formula and then multiply by 6 bc there are 6 little triangles in the hexagon

[@hiddenblue1598]

How come the apothem is 3?? 😅😅

[@livid91]

what is an altitude?

[@gadgetboyplaysmc]

height of the triangle basically. he created a line from the vertex of the hexagon to the base of one triangle and called that line the altitude.

[@BlueNitroTiger]

I'm in grade 10 and I find this very difficult and confusing.

[@princechristopher1133]

I am garage 5 I don’t know why I am here

[@joecaljack]

1st! wooohoooo

[@Lime_Mcoc]

Nice

[@seenvasreddy]

how do u get 2sqrt3 there

[@jaskaransingh6440]

the side of the hexagon is assumed 2sqrt3

[@pusplatam]

7:51

[@prasoonmbe]

I use Khan academy

[@jailai]

u lost me at the fractions 😭😭

[@abhinavmonga4946]

Lol 6.69 mil subs

[@mohitsinha6011]

dab

[@stormdraws1642]

i came for math​ help, i found someone with a pfp of Sebastian's demon eye, and im laughing, idk why, but I am

[@InfraredVision]

why is the 2Sq of 3 .. I'm trying to learn.. I don't know it that's the actual length, if so use a normal ###### number... of it it's a formula..

[@wendys2471]

I don't understand.

[@isabellewitthuhn8175]

Hehe I’m the 69th comment

[@humanbeeing4780]

NIC

[@KapilKumar-ke9sx]

Thoda hindi vaalo ka bhi dhyaan rakh lete angrej