PSLE OLMNP is part of a circle of radius 8 cm. OLN and OMP are quarter circles. The area of the shaded part OMN is 56 cm
2 and the perimeter of the shaded part OMN is 32 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 8 x 8
= 16π cm
2 Area of sector ONP
= 16π - 56
Area of figure OLMNP
= 16π + 16π - 56
= 32π - 56
≈ 44.5 cm
2 (Correct to 1 decimal place)
(b)
Length of arc MN
= 32 - 8 - 8
= 16 cm
Length of the arc of the quarter circle
=
14 x 2 x π x 8
= 4π cm
Length of arc NP
= (4π - 8) cm
Perimeter of the figure OLMNP
= 4π + 4π - 8 + 8 + 8
= 8π + 8
≈ 33.1 cm (Correct to 1 decimal place)
Answer(s): (a) 44.5 cm
2; (b) 33.1 cm