In triangle ABC, the angle bisector of angle BAC meets BC at D. If angle BAC=60 degrees, angle ABC=60 degrees and AD=24 then find the area of triangle ABC.
The triangle is equilateral...AD is a bisector and the altitude of ABC
A
24
B D C
Angle BAD = 30
BD = 24/sqrt 3
BC = 2 * 24 /sqrt 3 = 48/ sqrt 3 = 16sqrt 3
[ABC ] = (1/2) BC * AD = (1/2) (16sqrt 3) (24) = 192 sqrt 3
+2653 
