1. **State the problem:** We are given a parallelogram ABCD with sides AB = 15 cm and BC = 7 cm. We need to find the perimeter of ABCD. 2. **Recall the property of a parallelogram:** Opposite sides of a parallelogram are equal in length. Therefore, AB = CD and BC = DA. 3. **Calculate the perimeter:** The perimeter $P$ of a parallelogram is the sum of all its sides: $$P = AB + BC + CD + DA$$ Since $AB = CD = 15$ cm and $BC = DA = 7$ cm, substitute these values: $$P = 15 + 7 + 15 + 7$$ 4. **Simplify the expression:** $$P = (15 + 15) + (7 + 7) = 30 + 14 = 44$$ 5. **Final answer:** The perimeter of parallelogram ABCD is $44$ cm.