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CH-15-001 · Segment area and perimeter from a sector

OAB18 cm132°
Diagram not accurately drawn

O is the centre of a circle of radius 18 cm. Angle AOB is 132°. The shaded region is the minor segment bounded by chord AB and the minor arc AB. Calculate its area and perimeter. Give both answers to 2 decimal places.

Arcs, Sectors, Shaded Segment & Cosine/Sine Rule Booklet p. 37 & p. 38
Method
1) Segment area = Sector area ((θ/360)πr²) − Triangle area (½r² sin θ)
2) Segment perimeter = Arc length ((θ/360)2πr) + Chord length
Worked Example (CH-15-001)
1)
Sector area = 132360π(18)2\frac{132}{360}\pi(18)^2.
2)
Triangle area = 12(18)2sin⁡132∘\frac12(18)^2\sin 132^\circ.
3)
Segment area 252.83 cm².
4)
Chord AB = 2(18)sin⁡(132/2)∘2(18)\sin(132/2)^\circ.
5)
Perimeter = chord length + 1323602π(18)\frac{132}{360}2\pi(18).
6)
74.36 cm.
Ans = Area 252.83 cm²; perimeter 74.36 cm.