1. **State the problem:** We need to find the area of a trapezium with height 4 cm, bottom base 10 cm, and a top left segment of 3 cm. The trapezium has right angles at the top right corner and at the points where the height is marked. 2. **Identify the formula:** The area $A$ of a trapezium is given by the formula: $$A = \frac{(a + b)}{2} \times h$$ where $a$ and $b$ are the lengths of the two parallel sides (bases), and $h$ is the height (the perpendicular distance between the bases). 3. **Determine the lengths of the bases:** - The bottom base $b = 10$ cm. - The top base $a$ is the length of the top side. We know the top left segment is 3 cm, and since there is a right angle at the top right corner, the top base is the sum of the top left segment and the horizontal segment on the top right. 4. **Find the top base length:** Since the height is 4 cm and the trapezium has right angles, the horizontal segment on the top right is: $$10 - 3 = 7 \text{ cm}$$ So the top base $a = 3 + 7 = 10$ cm. 5. **Calculate the area:** $$A = \frac{(a + b)}{2} \times h = \frac{(10 + 10)}{2} \times 4$$ $$= \frac{20}{2} \times 4 = 10 \times 4 = 40$$ 6. **Final answer:** The area of the trapezium is $40$ square centimeters.