1. **State the problem:** We have a square-based pyramid with base edge length $5.7$ cm and volume $162.45$ cm$^3$. We need to find (a) the area of its base and (b) its height. 2. **Formula for volume of a square-based pyramid:** $$V = \frac{1}{3} \times \text{Base Area} \times \text{Height}$$ 3. **Calculate the area of the base:** Since the base is a square with edge length $5.7$ cm, $$\text{Base Area} = (5.7)^2 = 32.49 \text{ cm}^2$$ 4. **Calculate the height:** Using the volume formula, $$162.45 = \frac{1}{3} \times 32.49 \times h$$ Multiply both sides by 3: $$487.35 = 32.49 \times h$$ Divide both sides by 32.49: $$h = \frac{487.35}{32.49} = 15$$ 5. **Final answers:** - Area of base = $32.49$ cm$^2$ - Height = $15$ cm