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If ABCD is a square with side length a = 30, and b = 20, then what is the area of triangle CEF?

 

 Jan 5, 2021
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Let B   =(0,0)    let  F  = (30,20)

The slope ofthe segment BF  = ( 20/30)   = 2/3

 

So....the equation of a  line through BF  is  y =(2/3) x

 

And when y = 30  then

 

30= (2/3)x

 

x=  (3/2) 30   = 45

 

So  DE  =   45  - 30   = 15

 

And DF  =10

 

So....the area of   triangle DEC  =  (1/2)(DC)(DE) =  (1/2) (30) (15)  =   225

And the area of triangle DEF  =  (1/2) (DE) ( DF)  =   (1/2) (15)(10)  =  75

 

So area of CEF =   225 -  75   =    150

 

cool cool cool

 Jan 5, 2021

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