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#1**+1 **

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

CPhill Oct 15, 2018