Area of CDE = 1/3of area of AGD ?

84×3= AGD

AGD=252

Where I am wrong ?

Right here

area of CDE = \frac{CE * DE}{2}

area of AGD = \frac{AG * DG}{2} = \frac{3CE * 3DE}{2} = 9 * \frac{CE * DE}{2} = 9 * area CDE

This is not true.

They are similar triangles. Their sides are in **proportion**.

We can’t directly say that CDE is 1/3rd AGD.

So, from concept of similarity, AG = 3 * CE, DG = 3 * DE.

0.5 * CE * DE = 42

So, 0.5 * AG * DE = 9*42 = 378.