PSLE
OABCD is part of a circle of radius 13 cm. OAC and OBD are quarter circles. The area of the shaded part OBC is 104 cm² and the perimeter of the shaded part OBC is 39 cm. For each of the following, use the calculator value of π to find:

1. the area of the figure OABCD, correct to 1 decimal place,
2. the perimeter of the figure OABCD, correct to 1 decimal place.

(a)
Area of the quarter circle
= ¹₄ x π x 13 x 13
= 42.25π cm²

Area of sector OCD
= 42.25π - 104

Area of figure OABCD
= 42.25π + 42.25π - 104
= 84.5π - 104
≈ 161.5 cm² (Correct to 1 decimal place)

(b)
Length of arc BC
= 39 - 13 - 13
= 13 cm

Length of the arc of the quarter circle
= ¹₄ x 2 x π x 13
= 6.5π cm

Length of arc CD
= (6.5π - 13) cm

Perimeter of the figure OABCD
= 6.5π + 6.5π - 13 + 13 + 13
= 13π + 13
≈ 53.8 cm (Correct to 1 decimal place)

Answer(s): (a) 161.5 cm²; (b) 53.8 cm