Question

Find the area of an equilateral triangle (regular 3-gon) with the given measurement.

3-inch radius

A = sq. in.

Answer 1

Area= 1/2ap

Answer 2

I draw an auxiliary triangle off of the radius, the radius being the hypotenuse

Answer 3

By 3 inch radius, do you mean that it is inscribed in a circle of radius 3 inches?

Answer 4

The apothem is half of the radius

Answer 5

So it looks like both are drawings are similar?

Answer 6

So its 1.5

Answer 7

I multiply 1.5 times √3 to get the long side

Answer 8

Than i multiply that answer "3√3" by 2 to get the side of the big triangle

Answer 9

I multiply that by 3 to get the perimeter. So i have the perimeter and the apothem.

Answer 10

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.

Answer 11

The answer i got the first time is: 6 3/4√3 but they told me its wrong.

Answer 12

height = 1.5 x apothem = 1.5 x (r/2) = 3r/4.

Answer 13

I don't need the height to find the area though.

Answer 14

All i need is the apothem and the perimeter

Answer 15

You're right, you don't, but you can take advantage of some easy trigonometry to get the answer easier.

Answer 16

Ok, well i'm only in Geometry.. So i'm not suppose to be doing trig

Answer 17

*Well i don't know any

Answer 18

Ok, then I'll stop with that approach.

Answer 19

Lol, if it's fairly easy, I don't mind learning it

Answer 20

It must be easier than the book's method because everyone I talk to on here starts using trig

Answer 21

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.

Answer 22

I'll explain the methodology and you can do the work. It won't be that hard, really.

Answer 23

I got most of my questions right, but this one i got wrong and i'm not sure why.

Answer 24

We'll use apothem and perimeter and derive some cool measurements from them.

Answer 25

Groovy

Answer 26

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!

Answer 27

r= radius?

Answer 28

9/4 is the height?

Answer 29

yes.

Answer 30

Now, here's the trick, and it's really cool conceptually, but a little hard to explain. maybe I can draw a picture.

Answer 31

Ok.

Answer 32

For an equilateral triangle circumcentre, incentre , centroid are all at the same point

use this property to solve the problem

Answer 33

I forgot to put a letter at the top, call it c and call the, here, I'll draw again

Answer 34

@tcarroll010 , has given you the correct diagram, just name the angles and measures of sides

Answer 35

There.

Answer 36

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.