PSLE
The figure shows a path of width 4 m in a rectangular park of length 56 m. The outline of the path is made up of quarter circles with centre F, semicircles with centre J and straight lines. FG = HJ.

1. What is the width of the rectangular park?
2. Find the area of the path. Take π = 3.14

(a)
Length of 3 radii of the smaller circle + 2 widths of the path = 56 m

Length of 3 radii of the smaller circle
= 56 - 4 - 4
= 48 m

Radius of the smaller circles
= 48 ÷ 3
= 16 m

Width of the park
= 2 radii of the smaller circle + 2 widths of the path
= 2 x 16 + 2 x 4
= 40 m

(b)
Area of the path in one curve
= Area of the big quadrant - Area of the small quadrant

Radius of big quadrant
= 16 + 4
= 20 m

Area of the big quadrant
= ¹₄ x 3.14 x 20 x 20
= 314 m²

Area of the small quadrant
= ¹₄ x 3.14 x 16 x 16
= 200.96 m²

Area of the path in one curve
= 314 - 200.96
= 113.04 m²

Total path = 3 curves + 1 rectangle

Area of the rectangle
= 4 x 20
= 80 m²

Area of 3 curves
= 3 x 113.04
= 339.12 m²

Area of the path
= 339.12 + 80
= 419.12 m²

Answer(s): (a) 40 m; (b) 419.12 m²