PSLE OSTUV is part of a circle of radius 8 cm. OSU and OTV are quarter circles. The area of the shaded part OTU is 40 cm
2 and the perimeter of the shaded part OTU is 32 cm. For each of the following, use the calculator value of π to find:
- the area of the figure OSTUV, correct to 1 decimal place,
- the perimeter of the figure OSTUV, correct to 1 decimal place.
(a)
Area of the quarter circle
=
14 x π x 8 x 8
= 16π cm
2 Area of sector OUV
= 16π - 40
Area of figure OSTUV
= 16π + 16π - 40
= 32π - 40
≈ 60.5 cm
2 (Correct to 1 decimal place)
(b)
Length of arc TU
= 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 UV
= (4π - 8) cm
Perimeter of the figure OSTUV
= 4π + 4π - 8 + 8 + 8
= 8π + 8
≈ 33.1 cm (Correct to 1 decimal place)
Answer(s): (a) 60.5 cm
2; (b) 33.1 cm