A circular garden has radius 14 m. A chord subtends 60° at its centre, and the minor segment it cuts off is a flower bed. Find (i) the area of the bed, (ii) the area of the rest of the garden and (iii) the length of the fence around the bed. (Use π = 22/7 and √3 = 1.73)

1. 1 · Write what is given and what is to be found Given: r = 14 m, ∠AOB = 60°. To find: the area of the bed, the rest of the garden, and the fence length.
2. 2 · Draw the figure Circle with centre O; chord AB; radii OA and OB at 60°; shade the minor segment.
3. 3 · Write the formula or theorem Segment = (θ/360) × πr² − (√3/4) r² for 60°. Arc = (θ/360) × 2πr.
4. 4 · Find the sector Sector = (1/6) × (22/7) × 196 = (1/6) × 616 = 102.67 m².
5. 5 · Find the triangle ΔOAB is equilateral: area = (√3/4) × 196 = 49 × 1.73 = 84.77 m².
6. 6 · Find the two areas Flower bed = 102.67 − 84.77 = 17.90 m². Rest of the garden = 616 − 17.90 = 598.10 m².
7. 7 · Find the fence Arc = (1/6) × 88 = 14.67 m. Chord AB = 14 m (equilateral triangle). Fence = 14.67 + 14 = 28.67 m.
8. 8 · Check and box the answer Bed 17.90 m², rest 598.10 m², fence 28.67 m. The bed and the rest add up to 616 m².

Scoring tip: For the fence, remember the chord. The boundary of a segment is the arc plus the straight chord.