1. **Problem statement:** We have a prism with an equilateral triangular cross-section. The base of the triangle is 7 cm, and the prism's length (depth) is 8 cm. We need to find: a) The area of the shaded equilateral triangular face. b) The number of rectangular faces of the prism. c) The total area of these rectangular faces. 2. **Formulas and rules:** - Area of an equilateral triangle with side length $a$ is given by: $$\text{Area} = \frac{\sqrt{3}}{4} a^2$$ - A prism with a triangular base has 3 rectangular faces, each corresponding to one side of the triangle extended along the prism's length. - The area of each rectangular face is the side length multiplied by the prism's length. 3. **Calculations:** a) Area of the equilateral triangle: $$a = 7 \text{ cm}$$ $$\text{Area} = \frac{\sqrt{3}}{4} \times 7^2 = \frac{\sqrt{3}}{4} \times 49 = \frac{49\sqrt{3}}{4} \approx 21.22 \text{ cm}^2$$ b) Number of rectangular faces: Since the base is a triangle, the prism has 3 rectangular faces. c) Total area of the rectangular faces: Each rectangular face has area: $$7 \text{ cm} \times 8 \text{ cm} = 56 \text{ cm}^2$$ There are 3 such faces, so total area: $$3 \times 56 = 168 \text{ cm}^2$$ **Final answers:** a) Area of shaded face = $21.22$ cm$^2$ b) Number of rectangular faces = 3 c) Total area of rectangular faces = $168$ cm$^2$