1. The problem asks for the equation for the area of the base $B$ of a triangular prism. 2. The base is a right triangle with legs $x$ and $y$. 3. The formula for the area of a triangle is $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ 4. Since the triangle is right-angled, the legs $x$ and $y$ serve as the base and height. 5. Substitute $x$ and $y$ into the formula: $$B = \frac{1}{2} \times x \times y$$ 6. This formula gives the area of the triangular base $B$ of the prism. Final answer: $$B = \frac{1}{2}xy$$