PSLE
The figure shows a path of width 1 m in a rectangular park of length 11 m. The outline of the path is made up of quarter circles with centre S, semicircles with centre V and straight lines. ST = UV.

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 = 11 m

Length of 3 radii of the smaller circle
= 11 - 1 - 1
= 9 m

Radius of the smaller circles
= 9 ÷ 3
= 3 m

Width of the park
= 2 radii of the smaller circle + 2 widths of the path
= 2 x 3 + 2 x 1
= 8 m

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

Radius of big quadrant
= 3 + 1
= 4 m

Area of the big quadrant
= ¹₄ x 3.14 x 4 x 4
= 12.56 m²

Area of the small quadrant
= ¹₄ x 3.14 x 3 x 3
= 7.065 m²

Area of the path in one curve
= 12.56 - 7.065
= 5.495 m²

Total path = 3 curves + 1 rectangle

Area of the rectangle
= 1 x 4
= 4 m²

Area of 3 curves
= 3 x 5.495
= 16.485 m²

Area of the path
= 16.485 + 4
= 20.485 m²

Answer(s): (a) 8 m; (b) 20.485 m²