Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
Find the area of an equilateral triangle (regular 3gon) with the given measurement.
3inch radius
A = sq. in.
 one year ago
 one year ago
Find the area of an equilateral triangle (regular 3gon) with the given measurement. 3inch radius A = sq. in.
 one year ago
 one year ago

This Question is Closed

Dallasb22Best ResponseYou've already chosen the best response.0
I draw an auxiliary triangle off of the radius, the radius being the hypotenuse
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
By 3 inch radius, do you mean that it is inscribed in a circle of radius 3 inches?
 one year ago

Dallasb22Best ResponseYou've already chosen the best response.0
dw:1348254489061:dw
 one year ago

Dallasb22Best ResponseYou've already chosen the best response.0
The apothem is half of the radius
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
dw:1348254528658:dw So it looks like both are drawings are similar?
 one year ago

Dallasb22Best ResponseYou've already chosen the best response.0
I multiply 1.5 times √3 to get the long side
 one year ago

Dallasb22Best ResponseYou've already chosen the best response.0
Than i multiply that answer "3√3" by 2 to get the side of the big triangle
 one year ago

Dallasb22Best ResponseYou've already chosen the best response.0
I multiply that by 3 to get the perimeter. So i have the perimeter and the apothem.
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
Yes, 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.
 one year ago

Dallasb22Best ResponseYou've already chosen the best response.0
The answer i got the first time is: 6 3/4√3 but they told me its wrong.
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
height = 1.5 x apothem = 1.5 x (r/2) = 3r/4.
 one year ago

Dallasb22Best ResponseYou've already chosen the best response.0
I don't need the height to find the area though.
 one year ago

Dallasb22Best ResponseYou've already chosen the best response.0
All i need is the apothem and the perimeter
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
You're right, you don't, but you can take advantage of some easy trigonometry to get the answer easier.
 one year ago

Dallasb22Best ResponseYou've already chosen the best response.0
Ok, well i'm only in Geometry.. So i'm not suppose to be doing trig
 one year ago

Dallasb22Best ResponseYou've already chosen the best response.0
*Well i don't know any
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
Ok, then I'll stop with that approach.
 one year ago

Dallasb22Best ResponseYou've already chosen the best response.0
Lol, if it's fairly easy, I don't mind learning it
 one year ago

Dallasb22Best ResponseYou've already chosen the best response.0
It must be easier than the book's method because everyone I talk to on here starts using trig
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
No, 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.
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
I'll explain the methodology and you can do the work. It won't be that hard, really.
 one year ago

Dallasb22Best ResponseYou've already chosen the best response.0
I got most of my questions right, but this one i got wrong and i'm not sure why.
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
We'll use apothem and perimeter and derive some cool measurements from them.
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
We 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!
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
Now, here's the trick, and it's really cool conceptually, but a little hard to explain. maybe I can draw a picture.
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
dw:1348255695035:dw
 one year ago

psi9epsilonBest ResponseYou've already chosen the best response.0
For an equilateral triangle circumcentre, incentre , centroid are all at the same point use this property to solve the problem
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
I forgot to put a letter at the top, call it c and call the, here, I'll draw again
 one year ago

psi9epsilonBest ResponseYou've already chosen the best response.0
@tcarroll010 , has given you the correct diagram, just name the angles and measures of sides
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
dw:1348255924927:dw There.
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
We 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.
 one year ago

psi9epsilonBest ResponseYou've already chosen the best response.0
dw:1348255963318:dw
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
Sorry, I did ob wrong, but you can do it. It's 2/3 of oa.
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
Sorry, I'm trying to do 3 things at once, but it's right there in the diagram and just use pythagorean on the lengths.
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
2/3 of 9/4 so its 3/2
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
ob is 3/2 oa is 3/4, so you can get ab.
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
ab will be your base. ac your height. Then you can easily get area of triangle.
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
ac is 9/2 or (4 and 1/2)
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
oa 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
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
ob = oc = 3. So, you have a right triangle where you can figure out ab. ab^2 + oa^2 = ob^2
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
Once you get ab, it's a piece of cake.
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
Are you all set now?
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
I gotta go. I hope you are all set.
 one year ago

Dallasb22Best ResponseYou've already chosen the best response.0
No.. Lol, ab^2 + 3/4^2 =3^2?
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
I just got back to my computer after a half hour. You don't happen to still be there are you?
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
My 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.
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
oa 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).
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
Are you having trouble with the square root and getting ab? Is that the hangup?
 one year ago

Dallasb22Best ResponseYou've already chosen the best response.0
I don't think so, let me work out your equation above ^^
 one year ago

Dallasb22Best ResponseYou've already chosen the best response.0
OK, so i got: √6.75 So √6.75 times 4.5 = area? √6.75 = ab 4.5 = ac
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
yes, 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.
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
Because 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.
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
You should be able to get to that last number with what should be your upcoming and last step.
 one year ago

Dallasb22Best ResponseYou've already chosen the best response.0
So... 27√3  4 ???
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
yes, but more importantly, do you see the flow of the steps? That's the important thing.
 one year ago

Dallasb22Best ResponseYou've already chosen the best response.0
I can't carry that out?
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
You 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.
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
Decimalwise, it can be truncated to 11.69134.
 one year ago

Dallasb22Best ResponseYou've already chosen the best response.0
Oh wait sorry, 27√3/4 is the area!! Okay
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
yes, and area is ac x ab.
 one year ago

Dallasb22Best ResponseYou've already chosen the best response.0
I put the answer as: 27/4√3
 one year ago

Dallasb22Best ResponseYou've already chosen the best response.0
I'll let you know if they accept it in 5 minutes.
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
Not 27/4√3. It's \[27\sqrt{3}/4\]
 one year ago

tcarroll010Best ResponseYou've already chosen the best response.1
The order of those multiplicands is important.
 one year ago

Dallasb22Best ResponseYou've already chosen the best response.0
Correct Score: 100 Thank you!!
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.