1. **Problem statement:** We have a triangular prism with an equilateral triangle cross-section where each side of the triangle is 7 cm, and the length of the prism is 8 cm. We need to find: a) The area of the shaded rectangular face. b) The number of rectangular faces on the prism. c) The total area of all the rectangular faces. 2. **Formulas and important rules:** - The area of a rectangle is given by $\text{Area} = \text{length} \times \text{width}$. - An equilateral triangle has all sides equal and its height $h$ can be found using the formula: $$h = \frac{\sqrt{3}}{2} \times \text{side}$$ - A triangular prism has 3 rectangular faces corresponding to the 3 sides of the triangle, each with length equal to the prism's length. 3. **Step a) Area of the shaded face:** - The shaded face is one of the rectangular faces formed by one side of the triangle and the length of the prism. - The side length of the triangle is 7 cm, and the prism length is 8 cm. - Area of shaded face = $7 \times 8 = 56$ cm$^2$. 4. **Step b) Number of rectangular faces:** - Since the cross-section is a triangle, the prism has 3 rectangular faces, one for each side of the triangle. 5. **Step c) Total area of the rectangular faces:** - Each rectangular face has area = side length $\times$ prism length. - Since all sides are equal (7 cm), each rectangular face area = $7 \times 8 = 56$ cm$^2$. - Total area = $3 \times 56 = 168$ cm$^2$. **Final answers:** a) Area of shaded face = 56 cm$^2$. b) Number of rectangular faces = 3. c) Total area of rectangular faces = 168 cm$^2$.