PSLE
OPQRS is part of a circle of radius 8 cm. OPR and OQS are quarter circles. The area of the shaded part OQR is 56 cm² and the perimeter of the shaded part OQR is 48 cm. For each of the following, use the calculator value of π to find:

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

(a)
Area of the quarter circle
= ¹₄ x π x 8 x 8
= 16π cm²

Area of sector ORS
= 16π - 56

Area of figure OPQRS
= 16π + 16π - 56
= 32π - 56
≈ 44.5 cm² (Correct to 1 decimal place)

(b)
Length of arc QR
= 48 - 8 - 8
= 32 cm

Length of the arc of the quarter circle
= ¹₄ x 2 x π x 8
= 4π cm

Length of arc RS
= (4π - 8) cm

Perimeter of the figure OPQRS
= 4π + 4π - 8 + 8 + 8
= 8π + 8
≈ 33.1 cm (Correct to 1 decimal place)

Answer(s): (a) 44.5 cm²; (b) 33.1 cm