+0  
 
0
40
2
avatar

The diagram shows 3 identical regular hexagons with side length .7. If O_{1}, O_{2} O_{3} are their respective centers, what is the area of △O1​O2​O3​?

 

 Dec 29, 2020
 #1
avatar+114171 
+1

The distance. D.  from  the center of any  hexagon to its edge can ne found as

 

(1/2) side length  /  sin 30°  =   D /sin 60°

 

3.5 / (1/2) = D / (sqrt (3)  / 2)

 

7 (sqrt (3) / 2 )  = D

 

The  side   of   our  triangle is twice this  =   7sqrt (3)  

 

So....O1O2O3  forms an equilateral  triangle  with a side length of 7sqrt (3)

 

It's    area   =  (1/2) (7sqrt (3))^2  sqrt (3)  / 2   =    [ 147 sqrt (3)  /  4   ]   units^2

 

 

cool cool cool

 Dec 29, 2020
 #2
avatar
0

The diagram shows 3 identical regular hexagons with a side length .7. If O_{1}, O_{2} O_{3} are their respective centers, what is the area of △O1​O2​O3​?                                                                                    /\

                                                                                              is that  7  or  .7 ???

 Dec 30, 2020

36 Online Users

avatar
avatar
avatar