1. **Problem Statement:** We have a right prism with an equilateral triangle base of side length 7 cm and a prism height (length) of 8 cm. We need to find: a) The area of the shaded face (a rectangle with dimensions 7 cm by 8 cm). b) The number of rectangular faces of the prism. c) The total area of these rectangular faces. 2. **Formulas and Important Rules:** - Area of an equilateral triangle with side $a$ is given by: $$\text{Area} = \frac{\sqrt{3}}{4} a^2$$ - Area of a rectangle is: $$\text{Area} = \text{length} \times \text{width}$$ - A right prism with a triangular base has 3 rectangular faces, each corresponding to one side of the triangle, with height equal to the prism height. 3. **Step-by-step Solution:** **a) Area of the shaded face:** - The shaded face is a rectangle with dimensions 7 cm (side of triangle) and 8 cm (height of prism). - Calculate area: $$\text{Area} = 7 \times 8 = 56 \text{ cm}^2$$ **b) Number of rectangular faces:** - Since the base is a triangle with 3 sides, the prism has 3 rectangular faces. **c) Total area of the rectangular faces:** - Each rectangular face corresponds to one side of the triangle and has height 8 cm. - Each rectangle's area is side length $\times$ height. - Since all sides are equal (equilateral triangle), each rectangle has area: $$7 \times 8 = 56 \text{ cm}^2$$ - Total area of 3 rectangular faces: $$3 \times 56 = 168 \text{ cm}^2$$ **Final answers:** a) Area of shaded face = $56$ cm$^2$ b) Number of rectangular faces = $3$ c) Total area of rectangular faces = $168$ cm$^2$