PSLE OQRST is part of a circle of radius 11 cm. OQS and ORT are quarter circles. The area of the shaded part ORS is 55 cm
2 and the perimeter of the shaded part ORS is 44 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 11 x 11
= 30.25π cm
2 Area of sector OST
= 30.25π - 55
Area of figure OQRST
= 30.25π + 30.25π - 55
= 60.5π - 55
≈ 135.1 cm
2 (Correct to 1 decimal place)
(b)
Length of arc RS
= 44 - 11 - 11
= 22 cm
Length of the arc of the quarter circle
=
14 x 2 x π x 11
= 5.5π cm
Length of arc ST
= (5.5π - 11) cm
Perimeter of the figure OQRST
= 5.5π + 5.5π - 11 + 11 + 11
= 11π + 11
≈ 45.6 cm (Correct to 1 decimal place)
Answer(s): (a) 135.1 cm
2; (b) 45.6 cm