PSLE ODEFG is part of a circle of radius 8 cm. ODF and OEG are quarter circles. The area of the shaded part OEF is 32 cm
2 and the perimeter of the shaded part OEF is 24 cm. For each of the following, use the calculator value of π to find:
- the area of the figure ODEFG, correct to 1 decimal place,
- the perimeter of the figure ODEFG, correct to 1 decimal place.
(a)
Area of the quarter circle
=
14 x π x 8 x 8
= 16π cm
2 Area of sector OFG
= 16π - 32
Area of figure ODEFG
= 16π + 16π - 32
= 32π - 32
≈ 68.5 cm
2 (Correct to 1 decimal place)
(b)
Length of arc EF
= 24 - 8 - 8
= 8 cm
Length of the arc of the quarter circle
=
14 x 2 x π x 8
= 4π cm
Length of arc FG
= (4π - 8) cm
Perimeter of the figure ODEFG
= 4π + 4π - 8 + 8 + 8
= 8π + 8
≈ 33.1 cm (Correct to 1 decimal place)
Answer(s): (a) 68.5 cm
2; (b) 33.1 cm