Both statements are required to answer the question.
Statement I tells us that the triangle is an isosceles triangle. In an isoceles triangle, the altitude is also the median and bisects the third side. Hence, if we know the altitude length and the length of the congruent sides in an isoceles triangle, we can find its base. And if we know the base and the height of a triangle, we can find its area.
Option A is the Correct Answer.