1. **Stating the problem:** We have a metal strip of length 150 mm and height 20 mm. From this strip, three congruent trapeziums and two congruent parallelograms are pressed out. We need to find the unused area of the metal strip. 2. **Understanding the shapes and dimensions:** - Total strip dimensions: length = 150 mm, height = 20 mm. - Three trapeziums, each with height 20 mm, top base 15 mm, and bottom base 25 mm. - Two parallelograms, each with base 15 mm and height 20 mm. 3. **Formula for area of trapezium:** $$\text{Area} = \frac{(a+b)}{2} \times h$$ where $a$ and $b$ are the lengths of the two parallel sides, and $h$ is the height. 4. **Calculate area of one trapezium:** $$a = 15, \quad b = 25, \quad h = 20$$ $$\text{Area}_{\text{trapezium}} = \frac{(15 + 25)}{2} \times 20 = \frac{40}{2} \times 20 = 20 \times 20 = 400 \text{ mm}^2$$ 5. **Calculate total area of three trapeziums:** $$3 \times 400 = 1200 \text{ mm}^2$$ 6. **Formula for area of parallelogram:** $$\text{Area} = \text{base} \times \text{height}$$ 7. **Calculate area of one parallelogram:** $$\text{base} = 15, \quad \text{height} = 20$$ $$\text{Area}_{\text{parallelogram}} = 15 \times 20 = 300 \text{ mm}^2$$ 8. **Calculate total area of two parallelograms:** $$2 \times 300 = 600 \text{ mm}^2$$ 9. **Calculate total area of all pressed shapes:** $$1200 + 600 = 1800 \text{ mm}^2$$ 10. **Calculate total area of the metal strip:** $$\text{length} = 150, \quad \text{height} = 20$$ $$\text{Area}_{\text{strip}} = 150 \times 20 = 3000 \text{ mm}^2$$ 11. **Calculate unused area:** $$\text{Unused area} = \text{Area}_{\text{strip}} - \text{Area}_{\text{pressed}} = 3000 - 1800 = 1200 \text{ mm}^2$$ **Final answer:** The unused area of the metal strip is $1200$ mm$^2$.