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

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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[MissMeganMarie]

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

[nodariel]

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

[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.

[ShakkIsLife]

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

[ivanwarrior]

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

[zack_]

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!).

[alisabri]

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

[triggerguard]

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.

[rsimister]

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

[thedarklight]

people who need only the apothem go to 3:00

[faa]

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

[Karurosuki]

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

[alibenaissabenaissa]

Thanks you helped me alot with my homework

[SubscribersNoVids-lurg]

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

[ahkam]

I don't know why you can't prove it generally. Why you have taken side length = 2√3

[iluvbigbootie]

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

[kbling]

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

[MrTigerman]

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

[amjadmirza]

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

[boxhead]

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