Area Calculation in Triangle with Perpendicular Height

In triangle ABC, side AB measures 7 cm, side AC measures 10 cm, and angle A measures 45 degrees. Point D lies on side AC such that segment BD is perpendicular to segment AC. Calculate the area of triangle ABD.

Use the formula for the area of a triangle, which is $$Area = \f\frac{1}{2} \times base \times height$$, where the base is segment AC and the height is the length of segment BD.