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Six identical rectangles are placed inside a square with side 32 cm as shown. What is the area shaded in yellow?

 

 Dec 16, 2019
 #1
avatar+111321 
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Let the  longer side of the  small rectangle  = x

Let the shorter side   =  y

 

For the width of the square we have  that

 

x + ( x - y)  + x  + (x - y) = 32

4x - 2y  = 32

2x - y  = 16  ⇒  -2x + y = -16    (1)

 

For the  height of the square we have that

y  + x  +  y  + x + y  = 32

2x + 3y  = 32   (2)

 

Add  (1) and (2)  and we have that

4y  = 16

y = 4

And x = 10

 

We can decompose the yellow area  into  2 rectangles

One has a width  of   (32 - x)  and a height of  (x+ y)

So...its area  =  (32 - 10) ( 10 + 4)  = (22) (14)  =  308

 

And the other rectangle has a width of (x - y)  and a height of (x + y)

So.....its area  =  (10 - 4) ( 10 + 4) =  (6)(14)  =  84

 

So....the yellow area =  308 + 84  =   392 units^2

 

 

cool cool cool

 Dec 16, 2019
 #2
avatar+692 
0

Interesting math puzzle.smiley

 Dec 16, 2019

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