1. **State the problem:** We have a composite shape made of a triangle on top of a trapezium. The area of the triangle is given as 28 cm². The triangle's height is 7 cm, and the trapezium's height is 2 cm. The trapezium has a base of 5 cm. We need to find the area of the trapezium. 2. **Recall the formula for the area of a triangle:** $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ 3. **Find the base of the triangle:** Given the area of the triangle is 28 cm² and height is 7 cm, substitute into the formula: $$28 = \frac{1}{2} \times \text{base} \times 7$$ 4. **Solve for the base:** Multiply both sides by 2: $$2 \times 28 = \cancel{2} \times \frac{1}{\cancel{2}} \times \text{base} \times 7$$ $$56 = \text{base} \times 7$$ Divide both sides by 7: $$\frac{56}{\cancel{7}} = \text{base} \times \frac{\cancel{7}}{7}$$ $$8 = \text{base}$$ So, the base of the triangle is 8 cm. 5. **Understand the trapezium dimensions:** The trapezium shares the same top base as the triangle's base, which is 8 cm, and has a bottom base of 5 cm. Its height is 2 cm. 6. **Recall the formula for the area of a trapezium:** $$\text{Area} = \frac{1}{2} \times (\text{sum of parallel sides}) \times \text{height}$$ 7. **Calculate the area of the trapezium:** $$\text{Area} = \frac{1}{2} \times (8 + 5) \times 2$$ $$= \frac{1}{2} \times 13 \times 2$$ 8. **Simplify:** $$= \cancel{\frac{1}{2}} \times 13 \times \cancel{2}$$ $$= 13$$ **Final answer:** The area of the trapezium is 13 cm².