PSLE ONPQR is part of a circle of radius 10 cm. ONQ and OPR are quarter circles. The area of the shaded part OPQ is 80 cm
2 and the perimeter of the shaded part OPQ is 50 cm. For each of the following, use the calculator value of π to find:
- the area of the figure ONPQR, correct to 1 decimal place,
- the perimeter of the figure ONPQR, correct to 1 decimal place.
(a)
Area of the quarter circle
=
14 x π x 10 x 10
= 25π cm
2 Area of sector OQR
= 25π - 80
Area of figure ONPQR
= 25π + 25π - 80
= 50π - 80
≈ 77.1 cm
2 (Correct to 1 decimal place)
(b)
Length of arc PQ
= 50 - 10 - 10
= 30 cm
Length of the arc of the quarter circle
=
14 x 2 x π x 10
= 5π cm
Length of arc QR
= (5π - 10) cm
Perimeter of the figure ONPQR
= 5π + 5π - 10 + 10 + 10
= 10π + 10
≈ 41.4 cm (Correct to 1 decimal place)
Answer(s): (a) 77.1 cm
2; (b) 41.4 cm