1. **Problem Statement:** We have a metal strip composed of five trapezoidal shapes aligned horizontally with a total length of 150 mm and height 20 mm. We need to find the area of the metal strip unused. 2. **Given Dimensions:** - Total length: 150 mm - Height of each trapezoid: 20 mm - First trapezoid: top base = 15 mm, bottom base = 25 mm - Second trapezoid: top base = 15 mm, bottom base = 20 mm - Third trapezoid: height on right side = 15 mm (implying a trapezoid with one side shorter) - Fourth and fifth trapezoids: height = 20 mm, no other dimensions given 3. **Formula for Area of a Trapezoid:** $$\text{Area} = \frac{(a + b)}{2} \times h$$ where $a$ and $b$ are the lengths of the two parallel sides (bases), and $h$ is the height. 4. **Step-by-step Calculation:** - First trapezoid area: $$A_1 = \frac{(15 + 25)}{2} \times 20 = \frac{40}{2} \times 20 = 20 \times 20 = 400 \text{ mm}^2$$ - Second trapezoid area: $$A_2 = \frac{(15 + 20)}{2} \times 20 = \frac{35}{2} \times 20 = 17.5 \times 20 = 350 \text{ mm}^2$$ - Third trapezoid height is 15 mm on the right side, assuming the left side is 20 mm (same as others), and bases are unknown. Since no bases are given, we cannot calculate exact area, but if we assume it is a rectangle with height 15 mm and width equal to the difference in total length minus other trapezoids, we need more data. - Fourth and fifth trapezoids have height 20 mm but no base lengths given, so their areas cannot be calculated without additional information. 5. **Conclusion:** With the given data, only the first two trapezoids' areas can be calculated precisely. The total area of these two trapezoids is: $$A_1 + A_2 = 400 + 350 = 750 \text{ mm}^2$$ The total metal strip area (assuming height 20 mm and length 150 mm) is: $$A_{total} = 150 \times 20 = 3000 \text{ mm}^2$$ 6. **Unused area:** Assuming the trapezoids cover the metal strip fully except for the unknown parts, the unused area is: $$A_{unused} = A_{total} - (A_1 + A_2 + \text{areas of trapezoids 3,4,5})$$ Without dimensions for trapezoids 3, 4, and 5, the unused area cannot be exactly determined. **Summary:** More information is needed about trapezoids 3, 4, and 5 to find the unused metal strip area precisely.