+0  
 
+1
121
4
avatar

Three equilateral triangles with side lengths 3,6 and 4, respectively, are joined as shown. Find the area of the shaded region.

 

 Dec 21, 2019
 #1
avatar+109563 
+2

Note that  in  both shaded triangles.....the  angles  that  are touching the base of the  figure  must   = 60°

 

So  the shaded area ( a triangle)  on the left  =  (1/2) (6)(3)sin(60°)

 

And   the shaded area on the right (a riangle)  = (1/2) * (6) (4) sin (60°)

 

So....the total area of the two shaded regions  =

 

(1/2)(6)sin(60°)  [ 3 + 4 ]  =

 

3(√3/2)  [ 7]  =

 

 21√3

_____     units^2    ≈   18.19 units^2

     2

 

 

cool cool cool

 Dec 21, 2019
edited by CPhill  Dec 21, 2019
edited by CPhill  Dec 21, 2019
 #2
avatar
+1

 

I'm stuck trying to understand this. 

 

1.  How do you tell that the shaded triangles are right triangles?

2.  It looks like the 6 that you're multiplying by is the hypotenuse of those shaded triangles instead of the height.

 

I'm sorry for being so dense.

.

Guest Dec 21, 2019
 #4
avatar+109563 
+1

Sorry...I messed up......see  my edited answer above.....

 

 

cool cool cool

CPhill  Dec 21, 2019
edited by CPhill  Dec 21, 2019
 #3
avatar+531 
+1

The area of the triangle on the left is 7.794 units2, and the area of the triangle on the right is  10.394 units2.

Therefore, the total shaded area is:  18.188 units2

 Dec 21, 2019

59 Online Users

avatar
avatar
avatar
avatar