PSLE
ONPQR is part of a circle of radius 15 cm. ONQ and OPR are quarter circles. The area of the shaded part OPQ is 105 cm² and the perimeter of the shaded part OPQ is 75 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 15 x 15
= 56.25π cm²

Area of sector OQR
= 56.25π - 105

Area of figure ONPQR
= 56.25π + 56.25π - 105
= 112.5π - 105
≈ 248.4 cm² (Correct to 1 decimal place)

(b)
Length of arc PQ
= 75 - 15 - 15
= 45 cm

Length of the arc of the quarter circle
= ¹₄ x 2 x π x 15
= 7.5π cm

Length of arc QR
= (7.5π - 15) cm

Perimeter of the figure ONPQR
= 7.5π + 7.5π - 15 + 15 + 15
= 15π + 15
≈ 62.1 cm (Correct to 1 decimal place)

Answer(s): (a) 248.4 cm²; (b) 62.1 cm