PSLE OQRST is part of a circle of radius 9 cm. OQS and ORT are quarter circles. The area of the shaded part ORS is 63 cm
2 and the perimeter of the shaded part ORS is 45 cm. For each of the following, use the calculator value of π to find:
- the area of the figure OQRST, correct to 1 decimal place,
- the perimeter of the figure OQRST, correct to 1 decimal place.
(a)
Area of the quarter circle
=
14 x π x 9 x 9
= 20.25π cm
2 Area of sector OST
= 20.25π - 63
Area of figure OQRST
= 20.25π + 20.25π - 63
= 40.5π - 63
≈ 64.2 cm
2 (Correct to 1 decimal place)
(b)
Length of arc RS
= 45 - 9 - 9
= 27 cm
Length of the arc of the quarter circle
=
14 x 2 x π x 9
= 4.5π cm
Length of arc ST
= (4.5π - 9) cm
Perimeter of the figure OQRST
= 4.5π + 4.5π - 9 + 9 + 9
= 9π + 9
≈ 37.3 cm (Correct to 1 decimal place)
Answer(s): (a) 64.2 cm
2; (b) 37.3 cm