1. **Problem Statement:** Two cuboids each with dimensions 10m (length) × 8m (width) × 5m (height) are joined end to end. We need to find the Lateral Surface Area (LSA), Total Surface Area (TSA), and volume of the resulting solid. 2. **Understanding the problem:** When two cuboids are joined end to end along their length, the new length becomes the sum of the two lengths, while width and height remain the same. 3. **Dimensions of resulting solid:** - Length $L = 10 + 10 = 20$ m - Width $W = 8$ m - Height $H = 5$ m 4. **Formulas:** - Lateral Surface Area (LSA) of a cuboid = $2H(L + W)$ - Total Surface Area (TSA) of a cuboid = $2(LW + LH + WH)$ - Volume of a cuboid = $L \times W \times H$ 5. **Calculate LSA:** $$LSA = 2 \times 5 \times (20 + 8) = 10 \times 28 = 280 \text{ m}^2$$ 6. **Calculate TSA:** $$TSA = 2 \times (20 \times 8 + 20 \times 5 + 8 \times 5) = 2 \times (160 + 100 + 40) = 2 \times 300 = 600 \text{ m}^2$$ 7. **Calculate Volume:** $$Volume = 20 \times 8 \times 5 = 800 \text{ m}^3$$ **Final answers:** - LSA = 280 m² - TSA = 600 m² - Volume = 800 m³