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The figure shows two squares of sides 9 and 3, respectively. Find the area of the black region.

 

 Jan 22, 2021
 #1
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The height of the larger (white) right triangle at the  upper right   = 6

And the height of the  smaller  (white) right triangle at the  lower right  =  3

 

And these triangles are  siimilar

 

So the scale  factor  is  2:1

 

The legs of  the  smaller right triangle  are (1/3) (3)  =  1  and 3.....and its area =   (1/2)(3)(1)  = 3/2  = 1.5

 

The large  white region has the  area of   (1/2) ( 9) (3 + 9)  =   54

 

And the  combined area of the  squares =  9^2 + 3^2 =  90

 

So....the black area =   

 

90   -  54  - 1.5   = 

 

34.5  units^2

 

cool cool cool

 Jan 22, 2021
edited by CPhill  Jan 22, 2021

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