(a) [2 marks]

Area of outer sector \( = \frac{1}{2} \times 10^2 \times 5.2 = 260 \) cm² (M1)

Area of inner sector \( = \frac{1}{2} \times r^2 \times 5.2 = 2.6r^2 \) cm² (A1)

Shaded area \( = 260 – 2.6r^2 \) cm² (AG)

(b)(i) [2 marks]

Given area \( = 64 \) cm²: \( 260 – 2.6r^2 = 64 \) (M1)

Solving: \( r^2 = \frac{196}{2.6} \implies r \approx 8.68 \) cm (A1)

(b)(ii) [3 marks]

Outer arc length \( = 10 \times 5.2 = 52 \) cm (M1)

Inner arc length \( = 8.68 \times 5.2 \approx 45.14 \) cm (M1)

Straight edges \( = 2(10 – 8.68) = 2.64 \) cm

Total perimeter \( \approx 52 + 45.14 + 2.64 = 99.78 \) cm (3sf) (A1)