1. **Stating the problem:** We have a trapezoid ABCD with parallel sides AD and BC. Given are side AD = 5 cm, side AB = 12 cm, and the height (perpendicular distance from C to AB) = 4 cm. We need to find the area of the trapezoid. 2. **Formula for the area of a trapezoid:** $$\text{Area} = \frac{(\text{sum of parallel sides}) \times \text{height}}{2}$$ 3. **Identify the parallel sides:** The parallel sides are AD and BC. We know AD = 5 cm, but BC is not given directly. However, since AB = 12 cm and the height from C to AB is 4 cm, we can find BC by considering the right triangle formed. 4. **Find BC:** Since the height is perpendicular from C to AB, and AB = 12 cm, the length BC can be found by subtracting the base segment from AB. But since the problem does not provide the length of BC directly, and only the height and AB, we assume BC is parallel and equal to the segment at the top. 5. **Calculate the area:** Using the formula: $$\text{Area} = \frac{(AD + BC) \times \text{height}}{2}$$ Since BC is parallel and equal to the segment at the top, and given the height, the area is: $$\text{Area} = \frac{(5 + 12) \times 4}{2}$$ 6. **Simplify:** $$\text{Area} = \frac{17 \times 4}{2} = \frac{68}{2} = 34$$ **Final answer:** The area of trapezoid ABCD is $34$ square centimeters.