PSLE The figure shows a path of width 2 m in a rectangular park of length 25 m. The outline of the path is made up of quarter circles with centre K, semicircles with centre N and straight lines. KL = MN.
- What is the width of the rectangular park?
- Find the area of the path. Take π = 3.14
(a)
Length of 3 radii of the smaller circle + 2 widths of the path = 25 m
Length of 3 radii of the smaller circle
= 25 - 2 - 2
= 21 m
Radius of the smaller circles
= 21 ÷ 3
= 7 m
Width of the park
= 2 radii of the smaller circle + 2 widths of the path
= 2 x 7 + 2 x 2
= 18 m
(b)
Area of the path in one curve
= Area of the big quadrant - Area of the small quadrant
Radius of big quadrant
= 7 + 2
= 9 m
Area of the big quadrant
=
14 x 3.14 x 9 x 9
= 63.585 m
2 Area of the small quadrant
=
14 x 3.14 x 7 x 7
= 38.465 m
2 Area of the path in one curve
= 63.585 - 38.465
= 25.12 m
2 Total path = 3 curves + 1 rectangle
Area of the rectangle
= 2 x 9
= 18 m
2 Area of 3 curves
= 3 x 25.12
= 75.36 m
2 Area of the path
= 75.36 + 18
= 93.36 m
2 Answer(s): (a) 18 m; (b) 93.36 m
2