PSLE OMNPQ is part of a circle of radius 6 cm. OMP and ONQ are quarter circles. The area of the shaded part ONP is 42 cm
2 and the perimeter of the shaded part ONP is 24 cm. For each of the following, use the calculator value of π to find:
- the area of the figure OMNPQ, correct to 1 decimal place,
- the perimeter of the figure OMNPQ, correct to 1 decimal place.
(a)
Area of the quarter circle
=
14 x π x 6 x 6
= 9π cm
2 Area of sector OPQ
= 9π - 42
Area of figure OMNPQ
= 9π + 9π - 42
= 18π - 42
≈ 14.5 cm
2 (Correct to 1 decimal place)
(b)
Length of arc NP
= 24 - 6 - 6
= 12 cm
Length of the arc of the quarter circle
=
14 x 2 x π x 6
= 3π cm
Length of arc PQ
= (3π - 6) cm
Perimeter of the figure OMNPQ
= 3π + 3π - 6 + 6 + 6
= 6π + 6
≈ 24.8 cm (Correct to 1 decimal place)
Answer(s): (a) 14.5 cm
2; (b) 24.8 cm