1. **Problem Statement:** We have a rectangular prism with dimensions width = 4 mm, depth = 8 mm, and height = 11 mm. The top and bottom faces are shaded. We need to find: (a) The side lengths A, B, C, and D on the net. (b) The lateral surface area (excluding top and bottom). (c) The total surface area. 2. **Identify side lengths on the net:** - The net consists of 6 rectangles: top, bottom, front, back, left, and right faces. - Given the prism dimensions: - Height = 11 mm - Width = 4 mm - Depth = 8 mm - The top and bottom faces are rectangles of width × depth = 4 mm × 8 mm. - The sides of the net labeled A, B, C, D correspond to edges of the prism: - A = height = 11 mm - B = width = 4 mm - C = depth = 8 mm - D = height = 11 mm 3. **Calculate lateral surface area:** - Lateral surface area includes the four side faces (front, back, left, right), excluding top and bottom. - Formula for lateral surface area of a rectangular prism: $$\text{Lateral Surface Area} = 2 \times (\text{height} \times \text{width} + \text{height} \times \text{depth})$$ - Substitute values: $$= 2 \times (11 \times 4 + 11 \times 8)$$ $$= 2 \times (44 + 88)$$ $$= 2 \times 132$$ $$= 264$$ 4. **Calculate total surface area:** - Total surface area includes all 6 faces. - Formula: $$\text{Total Surface Area} = 2 \times (\text{width} \times \text{depth} + \text{height} \times \text{width} + \text{height} \times \text{depth})$$ - Substitute values: $$= 2 \times (4 \times 8 + 11 \times 4 + 11 \times 8)$$ $$= 2 \times (32 + 44 + 88)$$ $$= 2 \times 164$$ $$= 328$$ **Final answers:** - (a) A = 11 mm, B = 4 mm, C = 8 mm, D = 11 mm - (b) Lateral surface area = 264 mm² - (c) Total surface area = 328 mm²