1. **State the problem:** We need to find the area of the shaded section of a trapezium with a smaller right triangle inside it. 2. **Identify the shapes and dimensions:** - Large trapezium with parallel sides $25$ cm (top) and $15$ cm (bottom), height $14$ cm. - Smaller right triangle inside with base $11$ cm and height $6$ cm. 3. **Formula for the area of a trapezium:** $$\text{Area} = \frac{(a + b)}{2} \times h$$ where $a$ and $b$ are the lengths of the parallel sides, and $h$ is the height. 4. **Calculate the area of the trapezium:** $$\text{Area}_{\text{trapezium}} = \frac{(25 + 15)}{2} \times 14 = \frac{40}{2} \times 14 = 20 \times 14 = 280$$ 5. **Formula for the area of a triangle:** $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ 6. **Calculate the area of the smaller triangle:** $$\text{Area}_{\text{triangle}} = \frac{1}{2} \times 11 \times 6 = \frac{1}{2} \times 66 = 33$$ 7. **Calculate the shaded area by subtracting the triangle area from the trapezium area:** $$\text{Area}_{\text{shaded}} = 280 - 33 = 247$$ **Final answer:** The area of the shaded section is $247$ square centimeters.