Question

https://docs.google.com/document/d/185EhsdQdyNsSP4jTSfA2IhJ-6fA2jlZzZBbnuwKM_C8/edit?usp=sharing

I need a little help with this one. I drew the triangle, hope that helps! The question is on the document, anyone with link (you) can view it!

Answer 1

EVERYONE LEAVES

Answer 2

I'll try. I have to work through it a bit and come up with a way to solve it, first.

Answer 3

omg thank you

Answer 4

i can tell you the formulas that we studied on the sheet and maybe that will give you an idea. would that help?

Answer 5

That would probably help me find an approach that you'd recognize. I think I've found AN approach.

Answer 6

We are studying Area of a sector (measure of angle/360 (pi R^2)) and Arc Length (measure of angle/360 (2piR))

Answer 7

Yep, that fits with what I came up with. Great!

First, we need to choose an easy geometry to use for this problem. We see that there are three identical circles, arranged so they are touching (as in the figure). If we form a triangle with vertices at the CENTER of each triangle, what will the length of each of the sides be?

What type of triangle is it? What would be the angles of the triangle?

Answer 8

center of each circle, not each triangle.

Answer 9

that triangle would be equalateral and the side lenghts would b the radius (1 cm). the angles would all be 60*. Right?

Answer 10

Close. The side lengths would be 2cm (The radius of two circles)

Answer 11

What is the area of this triangle?

Answer 12

but you said the center of the circles. the distance from the center to the outside is 1/2 d.... oh nvm XDDDD

Answer 13

the area bcuz of the crazy formula is \[\sqrt{3}\]

Answer 14

Yep. Alright. Now, what's the area of each circle?

Answer 15

pir^2 and r of 1 so pi ?

Answer 16

Yep.

Almost done. We need to know how much area each circle "Takes out" of our triangle.

Each angle of the triangle is 60 degrees. For one circle, how much area does this correspond to?

Answer 17

1pi/6

Answer 18

Alright. We have all the pieces we need! Can you see how to get to the final answer?

Answer 19

no Xd

Answer 20

AH HA! sqr3 - 3pi/6! right?

Answer 21

Yep. Reduce your fraction, and you're done!

Good job!

Answer 22

omg thank u soooooo much!!!!

Answer 23

My pleasure :)

Don't get flustered by these types of questions. Just try to find some simple geometry that you can work through to find what you need. It gets easier with practice :)

Answer 24

thanks!