PSLE
OMNPQ is part of a circle of radius 9 cm. OMP and ONQ are quarter circles. The area of the shaded part ONP is 72 cm² and the perimeter of the shaded part ONP is 36 cm. For each of the following, use the calculator value of π to find:

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

(a)
Area of the quarter circle
= ¹₄ x π x 9 x 9
= 20.25π cm²

Area of sector OPQ
= 20.25π - 72

Area of figure OMNPQ
= 20.25π + 20.25π - 72
= 40.5π - 72
≈ 55.2 cm² (Correct to 1 decimal place)

(b)
Length of arc NP
= 36 - 9 - 9
= 18 cm

Length of the arc of the quarter circle
= ¹₄ x 2 x π x 9
= 4.5π cm

Length of arc PQ
= (4.5π - 9) cm

Perimeter of the figure OMNPQ
= 4.5π + 4.5π - 9 + 9 + 9
= 9π + 9
≈ 37.3 cm (Correct to 1 decimal place)

Answer(s): (a) 55.2 cm²; (b) 37.3 cm