PSLE OUVWX is part of a circle of radius 6 cm. OUW and OVX are quarter circles. The area of the shaded part OVW is 24 cm
2 and the perimeter of the shaded part OVW is 18 cm. For each of the following, use the calculator value of π to find:
- the area of the figure OUVWX, correct to 1 decimal place,
- the perimeter of the figure OUVWX, correct to 1 decimal place.
(a)
Area of the quarter circle
=
14 x π x 6 x 6
= 9π cm
2 Area of sector OWX
= 9π - 24
Area of figure OUVWX
= 9π + 9π - 24
= 18π - 24
≈ 32.5 cm
2 (Correct to 1 decimal place)
(b)
Length of arc VW
= 18 - 6 - 6
= 6 cm
Length of the arc of the quarter circle
=
14 x 2 x π x 6
= 3π cm
Length of arc WX
= (3π - 6) cm
Perimeter of the figure OUVWX
= 3π + 3π - 6 + 6 + 6
= 6π + 6
≈ 24.8 cm (Correct to 1 decimal place)
Answer(s): (a) 32.5 cm
2; (b) 24.8 cm