1. **State the problem:** We need to find the cost of the plastic sheet that will cover the bottom of a rectangular swimming pool. 2. **Identify the dimensions:** The pool is 4 metres wide and 5 metres long. 3. **Calculate the area of the pool's base:** The area $A$ of a rectangle is given by $$A = \text{length} \times \text{width}$$ 4. Substitute the given values: $$A = 5 \times 4 = 20 \text{ square metres}$$ 5. **Calculate the cost of the plastic:** The cost per square metre is 25. 6. Multiply the area by the cost per square metre: $$\text{Cost} = 20 \times 25 = 500$$ 7. **Final answer:** The least amount of plastic needed will cost 500.