PSLE
OGHJK is part of a circle of radius 11 cm. OGJ and OHK are quarter circles. The area of the shaded part OHJ is 66 cm² and the perimeter of the shaded part OHJ is 55 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 11 x 11
= 30.25π cm²

Area of sector OJK
= 30.25π - 66

Area of figure OGHJK
= 30.25π + 30.25π - 66
= 60.5π - 66
≈ 124.1 cm² (Correct to 1 decimal place)

(b)
Length of arc HJ
= 55 - 11 - 11
= 33 cm

Length of the arc of the quarter circle
= ¹₄ x 2 x π x 11
= 5.5π cm

Length of arc JK
= (5.5π - 11) cm

Perimeter of the figure OGHJK
= 5.5π + 5.5π - 11 + 11 + 11
= 11π + 11
≈ 45.6 cm (Correct to 1 decimal place)

Answer(s): (a) 124.1 cm²; (b) 45.6 cm