1. Problem 23: A wall is 4m high and a ladder is placed 3m from the foot of the wall. Find the length of the ladder. - This forms a right triangle with vertical height 4m and base 3m. - Use Pythagoras theorem: $$\text{Length} = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5$$ meters. 2. Problem 24: A bicycle wheel has a diameter of 42cm. Find its circumference. - Circumference of a circle: $$C=\pi d$$ - $$C = \pi \times 42 = 42\pi \approx 131.95$$ cm. 3. Problem 25: A cylindrical pipe has diameter 14cm and height 10cm. Find its capacity in litres. - Radius $$r= \frac{14}{2}=7$$ cm. - Volume $$V = \pi r^2 h = \pi \times 7^2 \times 10 = 490\pi \approx 1538.6$$ cubic cm. - Convert to litres: $$1 \text{ litre} = 1000 \text{ cm}^3$$ - Capacity = $$\frac{1538.6}{1000} = 1.5386$$ litres. 4. Problem 26: Area of trapezium with parallel sides 50cm and 40cm and height 25cm. - Area formula: $$\text{Area} = \frac{1}{2} (a+b)h$$ - $$= \frac{1}{2} (50 + 40) \times 25 = \frac{1}{2} \times 90 \times 25 = 1125$$ cm$^2$. 5. Problem 27: Find the shaded area between a large rectangle 50cm by 30cm and a smaller centered rectangle 20cm by 12cm inside it. - Area large rectangle: $$50 \times 30 = 1500$$ cm$^2$. - Area smaller rectangle: $$20 \times 12 = 240$$ cm$^2$. - Shaded area = $$1500 - 240 = 1260$$ cm$^2$. Final answers: - Ladder length: 5 m - Wheel circumference: $$42 \pi \approx 131.95$$ cm - Pipe capacity: approximately 1.54 litres - Trapezium area: 1125 cm$^2$ - Shaded area: 1260 cm$^2$