1. **Stating the problem:** We have a parallelogram ABCD with sides AB = 21 cm, BC = 25 cm, and angle BAD = 57°. 2. **Goal:** Find the length of the diagonal BD. 3. **Formula used:** In a parallelogram, the length of diagonal BD can be found using the law of cosines in triangle ABD: $$BD^2 = AB^2 + AD^2 - 2 \times AB \times AD \times \cos(\angle BAD)$$ 4. **Important note:** Since ABCD is a parallelogram, opposite sides are equal, so: $$AD = BC = 25 \text{ cm}$$ 5. **Substitute known values:** $$BD^2 = 21^2 + 25^2 - 2 \times 21 \times 25 \times \cos(57^\circ)$$ 6. **Calculate each term:** $$21^2 = 441$$ $$25^2 = 625$$ $$2 \times 21 \times 25 = 1050$$ 7. **Calculate cosine:** $$\cos(57^\circ) \approx 0.5446$$ 8. **Calculate the product:** $$1050 \times 0.5446 = 571.83$$ 9. **Calculate $BD^2$:** $$BD^2 = 441 + 625 - 571.83 = 1066 - 571.83 = 494.17$$ 10. **Find $BD$ by taking the square root:** $$BD = \sqrt{494.17} \approx 22.23 \text{ cm}$$ **Final answer:** The length of diagonal BD is approximately **22.23 cm**.