1. **Problem Statement:** We have a rectangular pyramid and a plane that cuts through the pyramid. The plane passes through the apex (vertex) of the pyramid and is perpendicular to the base. 2. **Understanding the Problem:** The plane slicing through the pyramid creates a cross-section. Since the plane is perpendicular to the base and passes through the apex, the cross-section will be a triangle. 3. **Key Formula:** The area of a triangle is given by: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ 4. **Applying the Formula:** - The base of the triangle is a segment on the base of the pyramid where the plane intersects. - The height of the triangle is the distance from the apex perpendicular to this base segment. 5. **Important Rules:** - The plane is perpendicular to the base, so the height of the triangle is along the height of the pyramid. - The base segment lies on the base of the pyramid. 6. **Intermediate Work:** - Identify the base segment length on the base where the plane cuts. - Use the pyramid's height as the height of the triangle. 7. **Conclusion:** The area of the cross-section triangle formed by the plane cutting through the apex and perpendicular to the base is: $$\text{Area} = \frac{1}{2} \times \text{(length of base segment)} \times \text{(height of pyramid)}$$ Without specific numerical values, this is the general solution approach.