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In the figure below, $ABDC,$ $EFHG,$ and $ASHY$ are all squares; $AB=EF =1$ and $AY=5$.

What is the area of quadrilateral $DYES$?

 

 

Guest Jun 27, 2018
 #1
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The area  of the two  small squares combined  is 2 units^2

 

Note that   CY  = AY  -  AC  =  AY - AB   =  5  - 1   =  4

And  CD  = AB  = 1

So...the area of triangle  CDY  = (1/2) CY * CD  =  (1/2) (4) ( 1)  =  2 units^2

 

And, by symmetry, triangles   BDS , YEG   and SEF will have the same area as triangle CDY

 

So...the area of quadrilateral DYES  =

 

Area  of square  ASHY  less  areas of the two smaller squares  less areas  of the four triangles  =

 

5^2  -  2 -   4 (2)  =

 

25  - 2  - 8  =

 

25  - 10  =

 

15 units^2

 

 

cool cool cool

CPhill  Jun 27, 2018

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