In the triangle ABC , Angle ACB = 90 degree (Angle Subtended by the Diameter = 90 degree)
AC = 5cm
AB = 6.5 * 2 = 13 cm
using Pythagoras theorem
$AB^{2} = AC^{2} + CB^{2}$
$CB = \sqrt{13^{2} - 5^{2}}$ = 12
Area of triangle ABC = 0.5 * AC * CB = 30 sq.cm.
Option B is the Correct Answer.