figure: ar-a1-clock.png The minute hand of a clock is 10.5 cm long and the hour hand is 7 cm long…

Step 1. The minute hand. It turns $\dfrac{45}{60} = \dfrac{3}{4}$ of a circle. Area $= \dfrac{3}{4} \times \dfrac{22}{7} \times 10.5^2 = \dfrac{3}{4} \times 346.5 = 259.875\ \text{cm}^2$.

Step 2. The hour hand. It turns $\dfrac{45}{720} = \dfrac{1}{16}$ of a circle. Area $= \dfrac{1}{16} \times \dfrac{22}{7} \times 7^2 = \dfrac{154}{16} = 9.625\ \text{cm}^2$.

Step 3. The total. $259.875 + 9.625 = 269.5\ \text{cm}^2$.