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Pentagon ABCDE has a vertical line of symmetry. What is the y-coordinate of vertex C so that the area of the pentagon is 50 square units?

 

 Dec 6, 2020
 #1
avatar+114221 
+1

Note  that   if we  connect BD  we have square  ABDE  with a side  = 4

So...its area =  side^2 =  4^2  = 16

 

y coordinate of  midpoint of BD =    4 

 

Then  the area of  triangle BDC =   50  - 16  =  34

 

So....the  area of this triangle = (1/2)  base  * height =  

 

(1/2) (BD) (height)   =   

 

(1/2)  (4) height  =   34       

 

2 * height =  34

 

height =  34/2    = 17

 

So.... C =   (2, y midpoint of BC + 17 )  =    (2, 4 + 17)   =  (2 , 21)

 

 

cool cool cool

 Dec 6, 2020
 #2
avatar+846 
+3

Coordinate      y = 4 + (50 - 42) / 2

 

 Dec 6, 2020

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