last question for the day

Triangles ADE, CD share the same base  (AC)

And triangles ADE and CDE  have the same altitudes...so....their bases are to each other as their areas

So  AD /DC  = 9/6   = 3/2

So...there are  5 equal parts of AC....and  AD  is 3 of them

So......AC / AD  =  5/3

Since triangles ADE and ABC are similar....the scale factor  of triangle  ABC to  triangle  ADE  is  (5/3)

So...  [ABC ] =  [scale factor of  ABC to ADE]^2  *  [ ADE ]  =

(5/3)^2 *  [ 9 ]  = 

25 / 9   *  [9]  =

25 units^2

Thank you Chris