+129771 We find AD as follows
BD^2 = AD^2 + AB^2 - 2(AD * AB) cos (60°)
6^2 = AD^2 + 5^2 - 2 (AD * 5) (1/2)
36 -25 = AD^2 -5AD
11 = AD^2 - 5AD
AD^2 - 5AD = 11
AD^2 - 5AD + 25/4 = 11 + 25/4
(AD - 5/2)^2 = [ 69 / 4]
AD - 5/2 = sqrt (69) / 2
AD = [ 5 + sqrt (69) ] / 2
The height = (5/2)sqrt (3) = 5sqrt (3)/2
Area = AD * height = [5sqrt (3)] / 2 * [ 5 + sqrt (69)] / 2 = 25sqrt(3) / 4 + 5sqrt [ 207] / 4 =
25sqrt (3) / 4 + 15sqrt (23) / 4 =
(5/4) [ 5sqrt (3) + 3 sqrt (23) ] ≈ 28.8
