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The smaller square in the diagram has side length 1. Equilateral triangles are constructed on its four sides, as shown. What is the area of the larger square?

 

Thanks in advance!!!

MIRB14  Jan 18, 2018
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2+0 Answers

 #1
avatar+85633 
+3

The area of the square is, of course, 1 square unit

 

Each of  equilateral triangles has a side of 1, so  their total area  is

 

4  (1/2) * 1^2  * sin (60)  =    2*√3/2  =  √3  square units

 

The other 4 triangles have two sides   of 1  and  an included angle between these sides  of 

[360 -  90 - 60 - 60  ]  =  150°

 

So...their area is

 

4 (1/2) * 1^2 * sin (150)  =  2 * (1/2)  =  1 square unit

 

So...the area  of  the larger square  is   ( 1  + 1 + √3)  =  [  2 + √3 ]  units^2

 

 

cool cool cool

CPhill  Jan 18, 2018
 #2
avatar+112 
+2

Thanks!

MIRB14  Jan 20, 2018

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