ABC is a triangle. AB = 5 cm, AC = √41 cm and BC = 8

Solution

In the triangle ABC as AB=5 and AD is perpendicular to BD and so triangle ABD and triangle ADC are right angled triangles AB=5 and so triangle ABD other sides may be 3 and 4 as BD=4 is not possible because if BD=4 then DC=4 the perpendicular is becoming also a bisector the the triangle ABC should be isosceles but it not the case so BD=3 and AD=4 and so DC=5 In triangle ADC also the condition satisfies and so area of the triangle ABD=(1/2)*3*4 =6 sq cm