PSLE OVWXY is part of a circle of radius 11 cm. OVX and OWY are quarter circles. The area of the shaded part OWX is 77 cm
2 and the perimeter of the shaded part OWX is 33 cm. For each of the following, use the calculator value of π to find:
- the area of the figure OVWXY, correct to 1 decimal place,
- the perimeter of the figure OVWXY, 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 OXY
= 30.25π - 77
Area of figure OVWXY
= 30.25π + 30.25π - 77
= 60.5π - 77
≈ 113.1 cm
2 (Correct to 1 decimal place)
(b)
Length of arc WX
= 33 - 11 - 11
= 11 cm
Length of the arc of the quarter circle
=
14 x 2 x π x 11
= 5.5π cm
Length of arc XY
= (5.5π - 11) cm
Perimeter of the figure OVWXY
= 5.5π + 5.5π - 11 + 11 + 11
= 11π + 11
≈ 45.6 cm (Correct to 1 decimal place)
Answer(s): (a) 113.1 cm
2; (b) 45.6 cm