1. **State the problem:** Riley wants to estimate the cost to lay a patio shaped like a trapezium with parallel sides 7 m and 4 m, and height 5 m. 2. **Calculate the area of the patio:** Use the formula for the area of a trapezium: $$\text{Area} = \frac{(a + b)h}{2}$$ where $a = 7$, $b = 4$, and $h = 5$. 3. **Substitute the values:** $$\text{Area} = \frac{(7 + 4) \times 5}{2} = \frac{11 \times 5}{2} = \frac{55}{2} = 27.5 \text{ m}^2$$ 4. **Find the median price per square metre:** Prices are: 85, 100, 75, 130, 150, 135. Sort them: 75, 85, 100, 130, 135, 150. Median is the average of the middle two values (100 and 130): $$\text{Median} = \frac{100 + 130}{2} = \frac{230}{2} = 115$$ 5. **Estimate the total cost:** Multiply the area by the median price: $$\text{Cost} = 27.5 \times 115 = 3162.5$$ **Final answer:** Riley estimates the patio will cost 3162.5.