I found that the base of triangle ABC is equal to 8 and that AB=AC because triangle ABD and triangle ACD are congruent, but I am confused about how to continue. Thanks for the help!
Triangle ABC is an isosceles triangle with a base equal to 8 units.
BD = CD = 4 DI = 3
∠B = 2(tan-1(3/4)) ≈ 73.74º
AD = tan(∠B) * BD = 13.7142857
[ABC] = BD * AD ≈ 54.857 square units