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What is the area of the shaded region in the figure below? Round your answer to the nearest square centimeter.

 Apr 7, 2019
 #1
avatar+8 
+1

Oh I just found the answer:

 

The two triangles that are shaded blue are similar.

So we have the following ratios:

3/3+9 = x/9

 

x=9/4

 

So height of the black triangle is 9 - 9/4 = 27/4

 

So area of black triangle is (9 * 27/4)/2 = 243/8

 

EDIT: here's the image

 Apr 7, 2019
edited by ng8165  Apr 7, 2019
 #2
avatar+101150 
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Let the bottom left  vertex of the small square be located at (0,0)

Let the top right vertex of the large square be located at  (12, 9)

So....the equation of the line connecting these two points  is  y = (9/12) x  ⇒ y =  (3/4)x     (1) 

The right edge of the small square lies on the line x = 3      (2)

 

So....subbing  (2) into (1)  we have that

 

y = (3/4)(3)  =  9/4

 

Then....the height of the shaded area   =   9 - 9/4  =   27/4 cm

And the width of the shaded area  = 9  cm

 

And since the shaded area is triangular, its area = 

 

(1/2) width * height  =

 

(1/2)(9)(27/4)  = 

 

(9/2)(27/4)   =

 

243/8  cm^2   =

 

30.375 cm^2

 

 

cool cool cool

 Apr 7, 2019
 #3
avatar+8 
+1

Thanks CPhill!

ng8165  Apr 7, 2019
 #4
avatar+101150 
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HAHAHA!!!!....your approach was better than mine....!!!!!

 

 

 

cool cool cool

CPhill  Apr 7, 2019

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