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Dallasb22
 2 years ago
Find the area of an equilateral triangle (regular 3gon) with the given measurement.
3inch radius
A = sq. in.
Dallasb22
 2 years ago
Find the area of an equilateral triangle (regular 3gon) with the given measurement. 3inch radius A = sq. in.

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Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.1I draw an auxiliary triangle off of the radius, the radius being the hypotenuse

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1By 3 inch radius, do you mean that it is inscribed in a circle of radius 3 inches?

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1348254489061:dw

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.1The apothem is half of the radius

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1348254528658:dw So it looks like both are drawings are similar?

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.1I multiply 1.5 times √3 to get the long side

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.1Than i multiply that answer "3√3" by 2 to get the side of the big triangle

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.1I multiply that by 3 to get the perimeter. So i have the perimeter and the apothem.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1Yes, and to make matters easier, the angle and segment bisectors will meet 2/3 of the way to the other side, making the height = 1.5 x apothem.

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.1The answer i got the first time is: 6 3/4√3 but they told me its wrong.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1height = 1.5 x apothem = 1.5 x (r/2) = 3r/4.

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.1I don't need the height to find the area though.

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.1All i need is the apothem and the perimeter

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1You're right, you don't, but you can take advantage of some easy trigonometry to get the answer easier.

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.1Ok, well i'm only in Geometry.. So i'm not suppose to be doing trig

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.1*Well i don't know any

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1Ok, then I'll stop with that approach.

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.1Lol, if it's fairly easy, I don't mind learning it

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.1It must be easier than the book's method because everyone I talk to on here starts using trig

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1No, that's ok. I can do it the other way. That's the way you're supposed to be doing it and it will blow others away.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1I'll explain the methodology and you can do the work. It won't be that hard, really.

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.1I got most of my questions right, but this one i got wrong and i'm not sure why.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1We'll use apothem and perimeter and derive some cool measurements from them.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1We can use one thing I said above, that height = 3r/4 because that does come from the apothem to radius relationship and the fact that angle and side bisectors meet in the middle and make that height 3r/4. Stop and draw yourself that on paper to convince yourself. Because that's going to be key. And grooviness is good here!

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1Now, here's the trick, and it's really cool conceptually, but a little hard to explain. maybe I can draw a picture.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1348255695035:dw

psi9epsilon
 2 years ago
Best ResponseYou've already chosen the best response.0For an equilateral triangle circumcentre, incentre , centroid are all at the same point use this property to solve the problem

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1I forgot to put a letter at the top, call it c and call the, here, I'll draw again

psi9epsilon
 2 years ago
Best ResponseYou've already chosen the best response.0@tcarroll010 , has given you the correct diagram, just name the angles and measures of sides

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1348255924927:dw There.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1We know ac = 9/4. We know oa is 3/4. We know ob is 3/4, so we can get ab and you can do 1/2 of h x b for oab. Then double for the whole triangle.

psi9epsilon
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1348255963318:dw

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1Sorry, I did ob wrong, but you can do it. It's 2/3 of oa.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1Sorry, I'm trying to do 3 things at once, but it's right there in the diagram and just use pythagorean on the lengths.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.12/3 of 9/4 so its 3/2

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1ob is 3/2 oa is 3/4, so you can get ab.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1ab will be your base. ac your height. Then you can easily get area of triangle.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1ac is 9/2 or (4 and 1/2)

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1oa is apothem which is 1/2 of r, so add 3 (which is oc) to 1 and 1/2 which is oa. so ac is 9/2

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1ob = oc = 3. So, you have a right triangle where you can figure out ab. ab^2 + oa^2 = ob^2

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1Once you get ab, it's a piece of cake.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1Are you all set now?

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1I gotta go. I hope you are all set.

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.1No.. Lol, ab^2 + 3/4^2 =3^2?

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1I just got back to my computer after a half hour. You don't happen to still be there are you?

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1My condolences. I'm thinking that you're not liking this problem anymore. I'm going to try to simplify it all in one post and you can just work from info in that and the diagram.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1oa is apothem and = r/2. oc=ob=r. ac=oc+oa. oa^2 + ab^2 = ob^2. Triangle area = ab x ac. That's all there is to it. My guess is that you're having trouble working with oa^2 + ab^2 = ob^2. So, for that ab: ab = sqrt(ob^2  oa^2).

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1Are you having trouble with the square root and getting ab? Is that the hangup?

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.1I don't think so, let me work out your equation above ^^

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.1OK, so i got: √6.75 So √6.75 times 4.5 = area? √6.75 = ab 4.5 = ac

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1yes, you're getting it, you really are. It might be a little better to think of that ab length, which is sqrt(6.75), as(3 x sqrt(3)) / 2. But either way works. Whatever is easier for you.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1Because when you're done, and you really almost are, enough that I can give you the answer, the area is (27 x sqrt(3)) / 4.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1You should be able to get to that last number with what should be your upcoming and last step.

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.1So... 27√3  4 ???

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1yes, but more importantly, do you see the flow of the steps? That's the important thing.

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.1I can't carry that out?

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1You can put it in decimal from or any other representation if you want. Sqrt(3) is irrational, so any decimal representation will truncate digits, but that's ok.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1Decimalwise, it can be truncated to 11.69134.

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.1Oh wait sorry, 27√3/4 is the area!! Okay

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1yes, and area is ac x ab.

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.1I put the answer as: 27/4√3

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.1I'll let you know if they accept it in 5 minutes.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1Not 27/4√3. It's \[27\sqrt{3}/4\]

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1The order of those multiplicands is important.

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.1Correct Score: 100 Thank you!!
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