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Segments \( \overline{CD}\) and \(\overline{AB}\) are parallel. If CD = 2, AB = 5, and [CDP] = 4, find [ABCD].

 

 Jan 30, 2021
 #1
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Since  [CDP ]  = 4

Then the area  is  (1/2) CD height  =   (1/2)(2) height  = (1/2) (2) (4)  =  4

So  the height  is 4

 

And  triangles   CDP  and ABP  are similar

So  the bases   are   5/2   = scale factor

So   height  of  ABP  =   ( 5/2) height of CDP  =  (5/2) (4)   = 10

 

So....the  whole height of   ABCD  =   10 +  4  = 14

 

And ABCD is a trapezoid....so its area  =

 

(1/2) (height)  ( sum of bases  AB + CD)  =

 

(1/2) ( 14) ( 5 + 2)   =

 

7  * 7   = 

 

49  = [ ABCD  ]

 

 

cool cool cool

 Jan 30, 2021
 #2
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Thanks a lot! This really clarified things for me!

Guest Jan 30, 2021

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