PSLE
OLMNP is part of a circle of radius 5 cm. OLN and OMP are quarter circles. The area of the shaded part OMN is 25 cm² and the perimeter of the shaded part OMN is 20 cm. For each of the following, use the calculator value of π to find:

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

(a)
Area of the quarter circle
= ¹₄ x π x 5 x 5
= 6.25π cm²

Area of sector ONP
= 6.25π - 25

Area of figure OLMNP
= 6.25π + 6.25π - 25
= 12.5π - 25
≈ 14.3 cm² (Correct to 1 decimal place)

(b)
Length of arc MN
= 20 - 5 - 5
= 10 cm

Length of the arc of the quarter circle
= ¹₄ x 2 x π x 5
= 2.5π cm

Length of arc NP
= (2.5π - 5) cm

Perimeter of the figure OLMNP
= 2.5π + 2.5π - 5 + 5 + 5
= 5π + 5
≈ 20.7 cm (Correct to 1 decimal place)

Answer(s): (a) 14.3 cm²; (b) 20.7 cm