Area of inscribed equilateral triangle (some basic trig used) | Circles | Geometry | Khan Academy

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Problem that requires us to figure out the area of an equilateral triangle inscribed in a circle (A little trigonometry used)
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[@rajeevk440]

If we use idea of 30 60 90 in smaller ∆s we will get h=2 p=1 b=✓3 For eq ∆ we can say base =2✓3, h=2+1 Now area of ∆ is (1/2)*(2✓3)(2+1) Area of ∆is 3✓3

[@ThomasMendenhall]

he solved this problem in 11 min. On my test im going to be needing to solve a whole bunch of these problems in 30 sec to a min. (o.O) nooooooo...

[@tanuvashisht1704]

Vidya Guru Reasoning tricks are also very good resource to raising speed in exams. I found them so easy for my most of the attempted questions.

[@rajveersingh-zg1es]

You commented here 8 years ago, what ya doing now?

[@shivanshjha938]

@@tanuvashisht1704 can u tell me where can I find that

[@ThomasMendenhall]

@@rajveersingh-zg1es filming a documentary to address misconceptions about the homeless population of Athens, GA and how the local government will attempt to help them with a legal encampment site.

[@Lavapurg]

​@@ThomasMendenhallhey atleast you're ready to calculate the area of the shaded region now if anyone asks you during your political documentary

[@mm22sapphire50]

this is beautiful i watch over and over again untill i understand exactly everything, and i dont have any exams closing by i just watch and learn it feels good

[@MsChocolisious]

or, to get the area of the triangle :- (sin120*2*2*1/2) x 3 :)

[@lonelywuffy]

So I did this problem before finishing the whole video. Got the same answer with LESS work. In geometry there's a lot of ways to do a problem. So what I did was find the area of the circle. Then since the triangle is equilateral, we know that the angles are 60 degrees. If we draw an apothem from the point of the circle, that will create a special triangle inside the equilateral triangle. A 30 60 90 triangle. We can use what we know about a 30 60 90 triangle stated in this video. The apothem is half of the hypotenuse which is 1. The other side will be square root 3. If the apothem bisects the chord, then chord A will be 2 square root 3. The area of the triangle is half of apothem times the perimeter. Perimeter will be 6 root 3. Area of triangle is 3 root three. So answer is 4 pie minus 3 root 3 UNITS squared. Don't forget the units because it is very important. Khan academy, I'm not doing this to challenge you, I'm asking is this a correct way. Or am I doing this wrong? Any help will be appreciated.

[@MrFigrepig]

what is wrong with for the trinangle base tines might

[@nickpower1837]

this video is the culmination of all the geometry rules i have learned

[@jeomaratas]

> 1/2(ab)sintheta (area triangle formula) > 1/2(2*2)sin120 = sqrt of 3 > sqrt of 3 * 3 = 3sqrt3 (Area of the whole Triangle) > another quick method :)

[@amazin356]

Thank you Sal your videos are very easy to understand unlike my teacher.

[@acekelor]

It's awesome but it had been rather good if you derived it for standard form

[@rajveersingh-zg1es]

you commented here 10 years ago.....

[@mahrukhnaqvi9700]

other than using trigonometry we could have solved it in less than two mins as we know that; the Side of a triangle inscribed in a circle = r x U.ROOT3 and the triangle inscribed in a circle is always equilateral, which means their Area is U.ROT3/4 x Side^sq. so simply subtract the area of the circle from the area of the triangle to get the area of the shaded region.

[@studytime7182]

That’s exactly what he did. He just explained how we got to know what the formula of a side actually is, and what the area of a triangle is

[@MeJustAimy]

i dont kno why or how u started these videos, but im soo grateful to u for doing so

[@KevZyro]

@mizzagirl217 this is 9th grade geometry.

[@hxhx5798]

how to solve?. Given: radius is given perimeter and area of triangle given. Circle is inscribed in triangle. neither isosceles nor equelateral. Find each side?

[@NinjaMinkzx]

@StavJazzMan You don't even need that! Use the equilateral triangle formula a^2 root 3 over 4

[@yashuppot3214]

That formula wasn’t made by god genius, it comes from trigonometry

[@kimgracyhaokip991]

My doubt clear thanks alot

[@isaacanwarwatts8844]

Can someone tell me how to prove that the midpoint of line a is halfway inbetween the radius and the edge of the circle?

[@angrypepecancer5205]

You can also use the Law of sine. a=2sin(120) ----------------- sin(30) =2 times the sq root of 3 the use the equalateral triangle formula.

[@lazybonez4909]

this is the big brain man

[@anirbanjyothisen9110]

PLEASE HELP ME WITH THIS SUM. The area of a n equilateral triangle is 49 cm2. Taking each angular point as centre, circles are drawn with radius equal to half length of the side of the triangle. Find the area of triangle not included in the circles? I NEED IT URGENTLY.

[@diyojenferhat]

thanks very much

[@pwnm0thers]

im in 6th grade and you helped me with fractions and other things thank you

[@shijimjob5772]

Dude it's been ten years😔. Time flies

[@priyankaw7016]

An equilateral triangle is inscribed in a circle. How many times is the area of the circle than the area of the triangle?;

[@laurabraga2758]

Don't need trigonometry!.. Even I got this using the space of a napkin and the 30:60:90 relationship. And I know I'm stupid. There is a right triangle which has the radio as hypotenuse and divides the 60 degree angle into two 30 degree angle, find the other side, and the height of the triangle is going to be this side plus the radios of the circle. The rest you know...

[@yashuppot3214]

The 30:60:90 relationship is literally trig?

[@divya.vishwakarma6895]

I had solved this question when I was in 3rd grade and I won prize..Because other student had performed the same method but I used trigonometry

[@towost2330]

r/thathappened

[@vitalienanu6395]

i am sure you did, buddy

[@theoyanto]

Yep was fun. ;)

[@manofallmasterofnone1020]

Lost me when you started using letters. Can we get a video with the use of numbers. I think it would be easier to follow. Its been 10+ years for me.

[@MrMss4]

@WindKayak Best of luck to you

[@aadilmiller3899]

can you provide me a link where i can find this kind of problems to solve for practice. please that would be a huge help.

[@norwayte]

It was fun.

[@syediqbal8197]

I must say it's a great video..

[@bjap1563]

@NinjaMinkzx right!!!!

[@denzel5274]

what if its not an equilateral triangle and its a half circle

[@IanB3rry]

Sakib Ahmed I learned quadratics, trig, and pre calc in seventh...

[@IanB3rry]

to your say something comment- sec(secant)=hypotenuse/opposite -cos(cosecant)=hypotenuse/adjacent -cot(cotangent)=adjacent/opposite okay i said something. You should also do some trig wave graphs those are fun. Maybe some summation notation( calculus version of addition) Not trying to boast but you shouldn't boast cause there is someone always smarter(not saying its me) now im in 8th grade

[@yashuppot3214]

@@IanB3rry Lmaoo weak, i learned quadratics before i even started algebra 1 and passed the ap calc test with a 5 in 8th grade.

[@Mado680]

the program u r using is called ?

[@vinodmahindru4560]

Very lengthy explanation could have been done mentally also

[@shadowking255]

that's pretty easy

[@MrTeacher2013]

great thanks:)

[@drevil37373]

im sorry but you made this way more complicated then it had to be, you know 2 is the raduis, then 30 60 90, you know the side opposite to 60 degrees is Bsqrt(3), side opposite to 30 degres is B. and Hyp is 2b, then you have 1= b. you know the length is of one side is twice that of the sqrt(3) as seen in diagram. so 2sqrt(3). you again using 30 60 90. can cut the triangle in half know base is sqrt(3). height is 3, multiple, /2 x2 cancel so 3*sqrt3 is the answer. lot easier.

[@beautydiva110]

What if it is not equilateral?

[@bobross3356]

you still do the same thing. just search for herons formula

[@sumitpal763]

What if triangle is scalene

[@anologclock]

you dont really need trig to determine the area....

[@artificialgd9286]

Why don't just use 30-60-90 triangles?

[@rajveersingh-zg1es]

11 years ago.....

[@VIKASGHODE]

Forget about video, you have really nice idea for earning money online. Energy point ahhh, nice concept. keep it on, but I suggest you to learn vedic math & geometry. You will forget this traditional approaches.( & Virtual positioning too)

[@GndmMkv]

@mizzagirl217 watch something easy this is like high school math

[@MrTeacher2013]

but the area is not 3sqrt{3} you had to fill it in. Right?

[@CedarAce1000]

Could you not (with O being the center of the circle, M being the midpoint of side a, and A being a point where the circle and triangle intersect) instead of using trigonometry and cosines instead say that OM is equal to AM-OA. Then you could use the pythagorean theorem to find everything. I solved this problem in ten minutes, being in seventh grade, using no trigonometry. I got that r=a/(4*sqrt3). Can anyone verify that this works and wasn't blind luck/

[@ChynaBryan]

Whats up wit these american comments? im american n im 13 taking geometry im not a nerd or anything and im watchin it perfectl fine. ima start saying this "sterotypical? probably foreign." cuz yal just tryyyyfliiin lolz

[@freydawg56]

Alright. Tell me all about SohCahToa then. In your own words. Then your statement will be valid.

[@yashuppot3214]

What do you mean in your own words lmao, they literally are ratios you cant explain them in your own words

[@vertorix8899]

yall know you could do 1/2aP right?

[@ojukusesay]

dats not fun.we find its real

[@erick_ftw]

s*** just got real

[@freydawg56]

you are in 6th grade and haven't studied trigonometry. watch something easier.

[@jmw1500]

Let me save you 11 minutes and trig functions that won't mean anything until you derive them in calculus. 2^2pi-(3*3^(1/2))

[@yashuppot3214]

Wrong lmao

[@benzappo1000]

im in 8th grade and know calc...

[@amr480a6]

2029 gang

[@benzappo1000]

im in 8th grade and know calc...