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\(We\ have\ triangle\ \triangle\ ABC\ where\ AB = AC\ and\ AD\ is\ an\ altitude.\ Meanwhile,\ E\ is\\ a\ point\ on\ AC\ such\ that\ AB\ \parallel DE.\ If \ BC\ =\ 12\ and\ the\ area\ of\\ \triangle ABC\ is \ 180,\ what\ is\ the\ area\ of\ ABDE?\)

 

Thank you in advance,

\(tommarvoloriddle\)

 Jul 25, 2019
edited by tommarvoloriddle  Jul 25, 2019
 #1
avatar+773 
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sorry tom i know this but i cant figure this out sorry

 Jul 25, 2019
 #2
avatar+1342 
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Then PM me this not post it as a ANSWER!

tommarvoloriddle  Jul 25, 2019
 #3
avatar+8725 
+5

This diagram has more information than I showed how to find. If you're unsure how to find, for example,  AD = 30, and want further explanation, just ask. smiley

 

 

m∠EDC  =  m∠ABC   because corresponding angles are congruent.

m∠ECD  =  m∠ACB   because they are the same angle

So by the AA similarity theorem,  △EDC ~ △ABC

 

When we draw a height to the base of an isosceles triangle, we split the base exactly in half.

So the scale factor from △ABC  to  △EDC  is  1/2.  And so...

area of △EDC  =  ( 1/2 )( 1/2 )( area of △ABC)

 

area of ABDE   =   area of △ABC - area of △EDC

area of ABDE   =   180 - ( 1/2 )( 1/2 )( 180 )

area of ABDE   =   180 - 45

area of ABDE   =   135

 

The areas are in square units.

 Jul 26, 2019
 #4
avatar+1342 
+7

Oh ok Thank you Hecticar!

tommarvoloriddle  Jul 26, 2019

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