PSLE
OEFGH is part of a circle of radius 13 cm. OEG and OFH are quarter circles. The area of the shaded part OFG is 78 cm² and the perimeter of the shaded part OFG is 52 cm. For each of the following, use the calculator value of π to find:

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

(a)
Area of the quarter circle
= ¹₄ x π x 13 x 13
= 42.25π cm²

Area of sector OGH
= 42.25π - 78

Area of figure OEFGH
= 42.25π + 42.25π - 78
= 84.5π - 78
≈ 187.5 cm² (Correct to 1 decimal place)

(b)
Length of arc FG
= 52 - 13 - 13
= 26 cm

Length of the arc of the quarter circle
= ¹₄ x 2 x π x 13
= 6.5π cm

Length of arc GH
= (6.5π - 13) cm

Perimeter of the figure OEFGH
= 6.5π + 6.5π - 13 + 13 + 13
= 13π + 13
≈ 53.8 cm (Correct to 1 decimal place)

Answer(s): (a) 187.5 cm²; (b) 53.8 cm