PSLE OLMNP is part of a circle of radius 6 cm. OLN and OMP are quarter circles. The area of the shaded part OMN is 30 cm
2 and the perimeter of the shaded part OMN is 24 cm. For each of the following, use the calculator value of π to find:
- the area of the figure OLMNP, correct to 1 decimal place,
- the perimeter of the figure OLMNP, correct to 1 decimal place.
(a)
Area of the quarter circle
=
14 x π x 6 x 6
= 9π cm
2 Area of sector ONP
= 9π - 30
Area of figure OLMNP
= 9π + 9π - 30
= 18π - 30
≈ 26.5 cm
2 (Correct to 1 decimal place)
(b)
Length of arc MN
= 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 NP
= (3π - 6) cm
Perimeter of the figure OLMNP
= 3π + 3π - 6 + 6 + 6
= 6π + 6
≈ 24.8 cm (Correct to 1 decimal place)
Answer(s): (a) 26.5 cm
2; (b) 24.8 cm