Figure 1 shows the sector OAB of a circle with centre O, radius 9 cm and angle 0.7 radians - Edexcel - A-Level Maths Pure - Question 7 - 2010 - Paper 3

The area of a sector can be calculated using the formula: $A = \frac{1}{2} r^2 \theta$ Substituting the values, we have: $A = \frac{1}{2} \times 9^2 \times 0.7 = \frac{1}{2} \times 81 \times 0.7 = 28.35 \text{ cm}^2$

Since line AC is perpendicular to OA, we can use the tangent function: $\tan(0.7) = \frac{AC}{9}$ Solving for AC, we have: $AC = 9 \times \tan(0.7)$ Calculating this value gives approximately: $AC \approx 9 \times 0.759 = 6.83 \text{ cm}$ Thus, to 2 decimal places, AC is $6.83$ cm.

The area of triangle AOC can be calculated using the formula: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ Here, the base is AC and the height is the radius OA. We already found AC above. Hence: $\text{Area} = \frac{1}{2} \times AC \times OA = \frac{1}{2} \times 6.83 \times 9$ This evaluates to: $\text{Area} \approx 30.67 \text{ cm}^2$ Thus, the area of H is approximately $30.67$ cm².