PSLE
The figure shows a path of width 5 m in a rectangular park of length 55 m. The outline of the path is made up of quarter circles with centre C, semicircles with centre F and straight lines. CD = EF.

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 = 55 m

Length of 3 radii of the smaller circle
= 55 - 5 - 5
= 45 m

Radius of the smaller circles
= 45 ÷ 3
= 15 m

Width of the park
= 2 radii of the smaller circle + 2 widths of the path
= 2 x 15 + 2 x 5
= 40 m

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

Radius of big quadrant
= 15 + 5
= 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 15 x 15
= 176.625 m²

Area of the path in one curve
= 314 - 176.625
= 137.375 m²

Total path = 3 curves + 1 rectangle

Area of the rectangle
= 5 x 20
= 100 m²

Area of 3 curves
= 3 x 137.375
= 412.125 m²

Area of the path
= 412.125 + 100
= 512.125 m²

Answer(s): (a) 40 m; (b) 512.125 m²