In an isosceles triangle ABC with AB=AC, AD and AE trisects BC such that BD = DE = EC. IF angle DAE is equal to angle ABC and the area of triangle ABC is equal to , then find AC.

Since AB = AC
Angle B = Angle C
Let BD = DE = EC = x
BD = EC = x, AB = AC and Angle B = Angle C
Triangle ABD is congruent to triangle ACE
AD = AE
Angle ADE = Angle AED
Now Angle ADE = Angle B + Angle BAD
Angle AED = Angle DAE + Angle BAD
Angle AED = Angle BAE
AB = AC = 2x
BC = 3x
Now you know all the sides of isosceles triangle, Calculate and equate the area and find x.