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In the shape above each yellow square has an area of 1 square unit. What is the area of the blue star?

 

 May 3, 2020
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Notice  that the diagonal of each of the yellow squares = sqrt (1^2 + 1^2)  = sqrt (2)

 

So....the width  of the yellow square at the top  = sqrt (2)

 

And if we draw a segment connecting  the bottom edges  of the two squares  directly adjacent to this top square we will form two (blue) right triangles  each with a base of   sqrt (2)  / 2    and a height of 1

So the area  of each of these triangles =  (1/2)( sqrt (2)/2) (1)  = sqrt (2)/4

 

And we have 8 such triangles ....so their total area  =  8 * sqrt (2) / 4   =  2sqrt (2)

 

And the remaining part  of the star  is just a square with a side length of sqrt (2)

So this area  =  (sqrt (2))^2  = 2

 

So....the total area of the blue star  =  2sqrt (2) + 2  =  2 (sqrt (2) + 1) ≈ 4.828 units^2

 

cool cool cool

 May 3, 2020

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