1. **Problem Statement:** Find the area of the cross section of a right prism where the cross section is a triangle with base BC and height AB. 2. **Given:** - Area of cross section formula: $$\text{Area} = \frac{1}{2} \times BC \times AB$$ 3. **Explanation:** The cross section is a triangle formed by edges BC and AB. To find its area, multiply the base BC by the height AB and then divide by 2. 4. **Step-by-step:** - Identify lengths BC and AB from the prism. - Calculate $$\frac{1}{2} \times BC \times AB$$. 5. **Final answer:** The area of the cross section is $$\frac{1}{2} \times BC \times AB$$. This formula is fundamental for calculating volume and surface area of the prism. --- 1. **Problem Statement:** Find the area of the cross section of a cylinder with radius $$r$$. 2. **Given:** - Area of cross section formula: $$\pi r^2$$ 3. **Explanation:** The cross section of a cylinder perpendicular to its height is a circle. The area of a circle is $$\pi$$ times the radius squared. 4. **Step-by-step:** - Identify the radius $$r$$ of the cylinder. - Calculate $$\pi r^2$$. 5. **Final answer:** The area of the cross section is $$\pi r^2$$. This is used to find volume and surface area of the cylinder.