1. **Problem statement:** We need to find the perimeter of trapezium ABCD with sides AB = 24 m, BC = 26 m, AD = 42 m, and angle at A and B are right angles. 2. **Understanding the trapezium:** Since AB and BC are perpendicular, and AD is vertical, ABCD is a right trapezium. 3. **Known sides:** AB = 24 m, BC = 26 m, AD = 42 m. 4. **Find side CD:** Since AD is vertical and BC is perpendicular to AB, side CD is the hypotenuse of a right triangle formed by the difference in vertical and horizontal lengths. 5. **Calculate horizontal length DC:** Horizontal length DC = AB - BC projection on AB. Since BC is perpendicular to AB, BC is vertical, so horizontal length DC = AB = 24 m. 6. **Calculate vertical length DC:** Vertical length DC = AD - BC = 42 m - 26 m = 16 m. 7. **Calculate length CD using Pythagoras theorem:** $$CD = \sqrt{(24)^2 + (16)^2} = \sqrt{576 + 256} = \sqrt{832} = 28.84 \text{ m (approx)}$$ 8. **Calculate perimeter:** $$\text{Perimeter} = AB + BC + CD + AD = 24 + 26 + 28.84 + 42 = 120.84 \text{ m}$$ **Final answer:** The perimeter of trapezium ABCD is approximately 120.84 m.