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Footpath — circular tiles
The figure shows a rectangular grass patch and an L-shaped footpath. The width of the footpath is 100 cm. The footpath is tiled using 38 circular tiles of diameter 50 cm, following the pattern shown. Each tile is in contact with those next to it.
- (a) What is the area of the footpath not covered by the tiles? (Take pi = 3.14)
- (b) What is the perimeter of the grass patch?
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About this method
One batch repeats. Work out one batch, then multiply.
In this one. Each 50 cm square of footpath loses the same corner area to its tile, so part (a) is one small subtraction done once and multiplied by 38 — never one big area minus 38 circles.
How to spot it
Items are described as a fixed group or ratio that repeats, such as tiles following a pattern, snacks sold in a fixed mix, or a rate given per hour or per item.
Common mistake
Children start from the grand total instead of first working out what one batch is worth. In rate questions they also confuse a duration with a clock time.
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