Question: The cross-section of this prism is a regular decagon. a) What is the area of each rectangular face? b) What is the total area of the rectangular faces? Shape: a regular decagonal prism is shown in the center of the page; the top edge is labeled $2$ cm, and the vertical height on the right is labeled $8$ cm.

1. **Problem Statement:** We have a regular decagonal prism with each side of the decagon base measuring $2$ cm and the height of the prism $8$ cm. We want to find: a) The area of each rectangular face. b) The total area of all the rectangular faces. 2. **Understanding the shape:** - A regular decagon has $10$ equal sides. - Each rectangular face corresponds to one side of the decagon and the height of the prism. 3. **Formula for the area of a rectangle:** $$\text{Area} = \text{length} \times \text{height}$$ 4. **Calculate the area of each rectangular face:** - Length of each rectangular face = side length of decagon = $2$ cm - Height of prism = $8$ cm $$\text{Area of each rectangular face} = 2 \times 8 = 16 \text{ cm}^2$$ 5. **Calculate the total area of all rectangular faces:** - Number of rectangular faces = number of sides of decagon = $10$ $$\text{Total area} = 10 \times 16 = 160 \text{ cm}^2$$ **Final answers:** a) Area of each rectangular face = $16$ cm$^2$ b) Total area of the rectangular faces = $160$ cm$^2$