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

Thank you in advance,

\(tommarvoloriddle\)

tommarvoloriddle Jul 25, 2019

#3**+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.

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.

hectictar Jul 26, 2019