1. **Problem statement:** Calculate the area of quadrilateral ABCD where angles at vertices A and C are right angles, and the sides are given as AD = 56 cm, AB = 33 cm, BC = 16 cm, and DC = 63 cm. 2. **Understanding the shape:** Since angles at A and C are right angles, ABCD can be divided into two right triangles: triangle ABD and triangle BCD. 3. **Formula for area of a right triangle:** $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ 4. **Calculate area of triangle ABD:** - At vertex A, angle is 90°, so sides AB and AD are perpendicular. - Base = AB = 33 cm, height = AD = 56 cm. - Area = $$\frac{1}{2} \times 33 \times 56 = \frac{1}{2} \times 1848 = 924$$ cm². 5. **Calculate area of triangle BCD:** - At vertex C, angle is 90°, so sides BC and DC are perpendicular. - Base = BC = 16 cm, height = DC = 63 cm. - Area = $$\frac{1}{2} \times 16 \times 63 = \frac{1}{2} \times 1008 = 504$$ cm². 6. **Total area of quadrilateral ABCD:** $$924 + 504 = 1428$$ cm². **Final answer:** The area of quadrilateral ABCD is $$1428$$ cm².