PSLE
ORSTU is part of a circle of radius 10 cm. ORT and OSU are quarter circles. The area of the shaded part OST is 80 cm² and the perimeter of the shaded part OST is 50 cm. For each of the following, use the calculator value of π to find:

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

(a)
Area of the quarter circle
= ¹₄ x π x 10 x 10
= 25π cm²

Area of sector OTU
= 25π - 80

Area of figure ORSTU
= 25π + 25π - 80
= 50π - 80
≈ 77.1 cm² (Correct to 1 decimal place)

(b)
Length of arc ST
= 50 - 10 - 10
= 30 cm

Length of the arc of the quarter circle
= ¹₄ x 2 x π x 10
= 5π cm

Length of arc TU
= (5π - 10) cm

Perimeter of the figure ORSTU
= 5π + 5π - 10 + 10 + 10
= 10π + 10
≈ 41.4 cm (Correct to 1 decimal place)

Answer(s): (a) 77.1 cm²; (b) 41.4 cm