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ABCD is a square with side length 2 cm. E is the midpoint of CD, and BF is perpendicular to AE. What is the area of ECBF, in square centimeters? Express your answer as a decimal to the nearest tenth.

 

 Jul 12, 2022
 #1
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F is also the midpoint of AD

 

Equation of line  containing   segment  AE  is

y = 2x

Equation of line containing segment BF  is

y = (-1/2)x + 1

 

Setting these equal  to get the x coordinate of the intersection of the segments

 

2x = (-1/2)x + 1

 

(5/2)x = 1

 

x = (2/5)

 

y =  2 (2/5)  = 4/5

 

Call the intersection pt   (2/5, 4/5)  = G

 

The area of right triangle DEF =  (1/2) (1) (1)   =1/2

Area of right  triangle AGB   = (1/2)(2)(4/5) = 4/5

Area of right triangle AFG =  (1/2)(2/5)(1)  =  1/5

 

Area of  ECBF =

  

Area of ABCD - Area of DEF - Area of AGB   - Area of AFG   =

 

2^2 - (1/2)  - (4/5) - (1/5)  =

 

4 - 1/2 - 1  =

 

2.5 cm^2

 

 

cool cool cool

 Jul 12, 2022

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