anonymous
  • anonymous
Find the area of an equilateral triangle (regular 3-gon) with the given measurement. 3-inch radius A = sq. in.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
Area= 1/2ap
anonymous
  • anonymous
I draw an auxiliary triangle off of the radius, the radius being the hypotenuse
anonymous
  • anonymous
By 3 inch radius, do you mean that it is inscribed in a circle of radius 3 inches?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
|dw:1348254489061:dw|
anonymous
  • anonymous
The apothem is half of the radius
anonymous
  • anonymous
|dw:1348254528658:dw| So it looks like both are drawings are similar?
anonymous
  • anonymous
So its 1.5
anonymous
  • anonymous
I multiply 1.5 times √3 to get the long side
anonymous
  • anonymous
Than i multiply that answer "3√3" by 2 to get the side of the big triangle
anonymous
  • anonymous
I multiply that by 3 to get the perimeter. So i have the perimeter and the apothem.
anonymous
  • anonymous
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.
anonymous
  • anonymous
The answer i got the first time is: 6 3/4√3 but they told me its wrong.
anonymous
  • anonymous
height = 1.5 x apothem = 1.5 x (r/2) = 3r/4.
anonymous
  • anonymous
I don't need the height to find the area though.
anonymous
  • anonymous
All i need is the apothem and the perimeter
anonymous
  • anonymous
You're right, you don't, but you can take advantage of some easy trigonometry to get the answer easier.
anonymous
  • anonymous
Ok, well i'm only in Geometry.. So i'm not suppose to be doing trig
anonymous
  • anonymous
*Well i don't know any
anonymous
  • anonymous
Ok, then I'll stop with that approach.
anonymous
  • anonymous
Lol, if it's fairly easy, I don't mind learning it
anonymous
  • anonymous
It must be easier than the book's method because everyone I talk to on here starts using trig
anonymous
  • anonymous
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.
anonymous
  • anonymous
I'll explain the methodology and you can do the work. It won't be that hard, really.
anonymous
  • anonymous
I got most of my questions right, but this one i got wrong and i'm not sure why.
anonymous
  • anonymous
We'll use apothem and perimeter and derive some cool measurements from them.
anonymous
  • anonymous
Groovy
anonymous
  • anonymous
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!
anonymous
  • anonymous
r= radius?
anonymous
  • anonymous
9/4 is the height?
anonymous
  • anonymous
yes.
anonymous
  • anonymous
Now, here's the trick, and it's really cool conceptually, but a little hard to explain. maybe I can draw a picture.
anonymous
  • anonymous
Ok.
anonymous
  • anonymous
|dw:1348255695035:dw|
anonymous
  • anonymous
For an equilateral triangle circumcentre, incentre , centroid are all at the same point use this property to solve the problem
anonymous
  • anonymous
I forgot to put a letter at the top, call it c and call the, here, I'll draw again
anonymous
  • anonymous
@tcarroll010 , has given you the correct diagram, just name the angles and measures of sides
anonymous
  • anonymous
|dw:1348255924927:dw| There.
anonymous
  • anonymous
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.
anonymous
  • anonymous
|dw:1348255963318:dw|
anonymous
  • anonymous
Sorry, I did ob wrong, but you can do it. It's 2/3 of oa.
anonymous
  • anonymous
ob is 2/3 of ac.
anonymous
  • anonymous
Ob is 2/3 of 3/4?
anonymous
  • anonymous
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.
anonymous
  • anonymous
I don't follow.
anonymous
  • anonymous
2/3 of 9/4 so its 3/2
anonymous
  • anonymous
1.5
anonymous
  • anonymous
ob is 3/2 oa is 3/4, so you can get ab.
anonymous
  • anonymous
ab will be your base. ac your height. Then you can easily get area of triangle.
anonymous
  • anonymous
Ab being 1.5√3
anonymous
  • anonymous
ac: 3
anonymous
  • anonymous
ac is 9/2 or (4 and 1/2)
anonymous
  • anonymous
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
anonymous
  • anonymous
Ahhh
anonymous
  • anonymous
ob = oc = 3. So, you have a right triangle where you can figure out ab. ab^2 + oa^2 = ob^2
anonymous
  • anonymous
Once you get ab, it's a piece of cake.
anonymous
  • anonymous
Are you all set now?
anonymous
  • anonymous
I gotta go. I hope you are all set.
anonymous
  • anonymous
No.. Lol, ab^2 + 3/4^2 =3^2?
anonymous
  • anonymous
I just got back to my computer after a half hour. You don't happen to still be there are you?
anonymous
  • anonymous
Sadly, i am.
anonymous
  • anonymous
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.
anonymous
  • anonymous
OK
anonymous
  • anonymous
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).
anonymous
  • anonymous
oa= 3/2 right?
anonymous
  • anonymous
yes
anonymous
  • anonymous
Are you having trouble with the square root and getting ab? Is that the hangup?
anonymous
  • anonymous
I don't think so, let me work out your equation above ^^
anonymous
  • anonymous
OK, so i got: √6.75 So √6.75 times 4.5 = area? √6.75 = ab 4.5 = ac
anonymous
  • anonymous
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.
anonymous
  • anonymous
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.
anonymous
  • anonymous
OKay.
anonymous
  • anonymous
You should be able to get to that last number with what should be your upcoming and last step.
anonymous
  • anonymous
So... 27√3 ------ 4 ???
anonymous
  • anonymous
\[27√3\div4\]
anonymous
  • anonymous
yes, but more importantly, do you see the flow of the steps? That's the important thing.
anonymous
  • anonymous
I can't carry that out?
anonymous
  • anonymous
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.
anonymous
  • anonymous
Decimal-wise, it can be truncated to 11.69134.
anonymous
  • anonymous
Oh wait sorry, 27√3/4 is the area!! Okay
anonymous
  • anonymous
yes, and area is ac x ab.
anonymous
  • anonymous
I put the answer as: 27/4√3
anonymous
  • anonymous
I'll let you know if they accept it in 5 minutes.
anonymous
  • anonymous
Not 27/4√3. It's \[27\sqrt{3}/4\]
anonymous
  • anonymous
The order of those multiplicands is important.
anonymous
  • anonymous
Ok
anonymous
  • anonymous
Correct Score: 100 Thank you!!

Looking for something else?

Not the answer you are looking for? Search for more explanations.