WAEC 2022 · Paper 2 · Q3

Plane mensuration
Trigonometric ratios

A chord subtends an angle of $72^\circ$ at the centre of a circle of radius $24.5\text{ m}$ . Calculate the perimeter of the minor segment. $\left[\text{Take }\pi = \frac{22}{7}\right]$

(a)
Perimeter (m, 1 d.p.)

Worked solution (try it first)

The perimeter of a segment is its chord plus its arc.
The perpendicular from the centre bisects the chord and the $72^\circ$ angle, so half the chord is $24.5\sin 36^\circ \approx 14.40$ m and the chord is about $28.80$ m.
Arc $= \frac{72}{360} \times 2 \times \frac{22}{7} \times 24.5$
$= 30.8$ m.
Perimeter $\approx 28.80 + 30.8 = 59.6$ m.

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