PSLEThe figure shows a rectangular grass patch and an L-shaped footpath. The width of the footpath is 40 cm. The footpath is tiled using 76 circular tiles of diameter 20 cm, following the pattern shown. Each tile is in contact with those next to it.
- What is the area of the footpath not covered by the tiles? Take π = 3.14.
- What is the perimeter of the grass patch?
(a)
Area of a circular tile
= 3.14 x 10 x 10
= 314 cm
2 Area of a square plot that is under a circular tile
= 20 x 20
= 400 cm
2Area of the footpath not covered by a circular tile
= 400 - 314
= 86 cm
2 Area of the footpath not covered by all the tiles
= 86 x 76
= 6536 cm
2 (b)
Number of circular tiles touching the 2 lengths of the grass patch
= (76 - 4) ÷ 2
= 72 ÷ 2
= 36
Perimeter of the grass patch
= 2 x 36 x 20
= 1440 cm
Answer(s): (a) 6536 cm
2; (b) 1440 cm