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In the figure below, ABDC, EFHG, and ASHY are all squares; and AB = EF = 1 and AY = 6.  What is the area of quadrilateral DYES?

 

 Dec 3, 2020
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AC = AB  = 1

CY  =   AY - AC = 6 - 1 =  5

 

Area of square ASHY  = (AC + CY)^2  =  (1 + 5)^2  =   6^2   = 36

 

Area of  2 smaller squares = 2 (1)^2 =  2

 

Triangles  CDY,  YEG, EFS  and SDB  are congruent,,,,each has a base of  5 and a height of 1

So....their combined area =  4 (1/2) (5) (1)   =  10

 

Area of DYES  = 

 

36 - 2  - 10   =   24

 

 

cool cool cool

 Dec 3, 2020

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