PSLE
ONPQR is part of a circle of radius 8 cm. ONQ and OPR are quarter circles. The area of the shaded part OPQ is 64 cm² and the perimeter of the shaded part OPQ is 32 cm. For each of the following, use the calculator value of π to find:

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

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

Area of sector OQR
= 16π - 64

Area of figure ONPQR
= 16π + 16π - 64
= 32π - 64
≈ 36.5 cm² (Correct to 1 decimal place)

(b)
Length of arc PQ
= 32 - 8 - 8
= 16 cm

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

Length of arc QR
= (4π - 8) cm

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

Answer(s): (a) 36.5 cm²; (b) 33.1 cm