Area of paths crossing a garden
A school garden has two paths crossing in the middle, one along it and one across. Change the garden's size, the paths' width and the paving price, and find the area of the paths, the lawn left and the cost.
Core concept
Two crossing paths w wide cover w × l + w × b − w², because the square where they meet would otherwise be counted twice; the lawn is the rest
Topic: Area
A garden l long and b broad has two paths, each w wide: one runs along the length and one across the breadth, and they cross in the middle. The path along the garden is a rectangle l × w; the one across is b × w. Adding them counts the small square in the middle, w × w, twice, so we take it away once: area: How much flat space a shape covers, measured in square units like cm². All key words of the paths = w(l + b) − w². The lawn is what is left: l × b − the paths. To pave the paths, the cost is the area × the rate in rupees per m².
What you will learn
- Find the area of two crossing paths as w(l + b) − w².
- Explain why the square where the paths meet is taken away once.
- Find the area left over and the cost of paving.
Before you start
- Know the area of a rectangle and a square.
Materials
- Squared paper and coloured pencils
Equipment
- A measuring tape
Procedure
- Record a 30 m × 20 m garden with 2 m paths at Rs 150 per m².
- Make the paths 3 m wide and record.
- Make the garden 40 m × 25 m and record.
- Change the paving to Rs 200 per m² and record.
How this simulation is simplified
- The paths are straight, run parallel to the sides and cross in the middle.