PSLE
OGHJK is part of a circle of radius 12 cm. OGJ and OHK are quarter circles. The area of the shaded part OHJ is 60 cm² and the perimeter of the shaded part OHJ is 36 cm. For each of the following, use the calculator value of π to find:

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

(a)
Area of the quarter circle
= ¹₄ x π x 12 x 12
= 36π cm²

Area of sector OJK
= 36π - 60

Area of figure OGHJK
= 36π + 36π - 60
= 72π - 60
≈ 166.2 cm² (Correct to 1 decimal place)

(b)
Length of arc HJ
= 36 - 12 - 12
= 12 cm

Length of the arc of the quarter circle
= ¹₄ x 2 x π x 12
= 6π cm

Length of arc JK
= (6π - 12) cm

Perimeter of the figure OGHJK
= 6π + 6π - 12 + 12 + 12
= 12π + 12
≈ 49.7 cm (Correct to 1 decimal place)

Answer(s): (a) 166.2 cm²; (b) 49.7 cm