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Segments CD  and AB are parallel. If CD = 2, AB = 4, and [CDP] = 5, find [ABCD].

 

 Jun 8, 2022
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Triangles CPD  and  APB  are similar

 

The scale factor  between these  is   (4/2)   = 2

 

So....the area of triangle  APB  = [ CPD] * 2^2  =  5 * 2^2  = 20

 

Next...the  height of triangle   CDP  can be found as 

5 =(1/2) 2 * h  

h =  5

 

So....the height of triangle APB is twice this  =  10

 

So.....the total height of the figure =  5 + 10  =  15

 

And the area of triangle  CPB  = area of triangle  CDB  - area of triangle CPD  =

 

(1/2) (CD) * height of figure    - [ CPD]   =  (1/2)(2)(15)  -  5   =  10

 

And [CPB ]  = [ DPA]

 

 

So.....the total area  of the figure =  [ CPB] + [ APB ] + [ CPB ] + [ DPA]  =

 

5 + 20 + 10 + 10  = 

 

45  =    [ABCD ] 

 

cool cool cool

 Jun 8, 2022

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