PSLE
ODEFG is part of a circle of radius 6 cm. ODF and OEG are quarter circles. The area of the shaded part OEF is 42 cm² and the perimeter of the shaded part OEF is 36 cm. For each of the following, use the calculator value of π to find:

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

(a)
Area of the quarter circle
= ¹₄ x π x 6 x 6
= 9π cm²

Area of sector OFG
= 9π - 42

Area of figure ODEFG
= 9π + 9π - 42
= 18π - 42
≈ 14.5 cm² (Correct to 1 decimal place)

(b)
Length of arc EF
= 36 - 6 - 6
= 24 cm

Length of the arc of the quarter circle
= ¹₄ x 2 x π x 6
= 3π cm

Length of arc FG
= (3π - 6) cm

Perimeter of the figure ODEFG
= 3π + 3π - 6 + 6 + 6
= 6π + 6
≈ 24.8 cm (Correct to 1 decimal place)

Answer(s): (a) 14.5 cm²; (b) 24.8 cm