PSLE
OQRST is part of a circle of radius 12 cm. OQS and ORT are quarter circles. The area of the shaded part ORS is 84 cm² and the perimeter of the shaded part ORS is 48 cm. For each of the following, use the calculator value of π to find:

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

(a)
Area of the quarter circle
= ¹₄ x π x 12 x 12
= 36π cm²

Area of sector OST
= 36π - 84

Area of figure OQRST
= 36π + 36π - 84
= 72π - 84
≈ 142.2 cm² (Correct to 1 decimal place)

(b)
Length of arc RS
= 48 - 12 - 12
= 24 cm

Length of the arc of the quarter circle
= ¹₄ x 2 x π x 12
= 6π cm

Length of arc ST
= (6π - 12) cm

Perimeter of the figure OQRST
= 6π + 6π - 12 + 12 + 12
= 12π + 12
≈ 49.7 cm (Correct to 1 decimal place)

Answer(s): (a) 142.2 cm²; (b) 49.7 cm