+128 We know $\overline {DE}\parallel \overline {BC}.$ Given $[ADE]=9$ and $[CDE]=6,$ find $[ABC].$
https://latex.artofproblemsolving.com/6/4/2/6426d0d7650c668b5b900bdc52c9030f0880d2bb.png
+129849 [ ADE] and [ CDE] are on the same base, ED
Therefore..since [CDE] = 6 and [ADE] = 9 ...the height of [CDE] must be (6/9) = (2/3) the height of [ ADE]
Therfore the height of [ABC] = height of ADE + (2/3)height of ADE = (5/3) ADE
And since DE is parallel to AB then [AED] and [ ABC] are similar
So... [ ABC] = (5/3)^2 * area of [ AED] = (25/9)(9) = 25
