1. **Stating the problem:** We have a rectangular piece of wood measuring 430 cm by 42 cm. From this, wooden pieces for two identical bookcases are cut. We need to find the area of the remaining wood after cutting the required pieces. 2. **Calculate the total area of the original wood:** $$\text{Area}_{\text{original}} = 430 \times 42 = 18060 \text{ cm}^2$$ 3. **Determine the area of wood used for one bookcase:** From the problem, the wooden pieces correspond to the top, bottom, sides, and shelves. Using the dimensions from the diagrams (not provided here but implied), assume the total wood area used for one bookcase is calculated or given. Since the problem does not specify exact dimensions for each piece, we will calculate based on the total wood used for two bookcases. 4. **Calculate the total wood area used for two bookcases:** Let the total wood area used for two bookcases be $A_{used}$. This is the sum of the areas of all wooden pieces for two bookcases. 5. **Calculate the remaining wood area:** $$\text{Area}_{\text{remaining}} = \text{Area}_{\text{original}} - A_{used}$$ 6. **Final answer:** Since the exact dimensions of the wooden pieces are not provided in the prompt, the problem cannot be fully solved without that data. However, the method to find the remaining area is as above. If the total wood used for two bookcases is known, substitute it into step 5 to find the remaining area.