Paths, Cross-sections and Cost
The applied mensuration questions: a path running around or through a field, a room to be tiled, painted or carpeted at a given rate, the number of tiles or bricks, and how long a pipe takes to fill a tank.
What you will be able to do
- Find the area of a path by subtracting an inner rectangle from an outer one.
- Handle two crossing roads through a field without double-counting the overlap.
- Turn an area and a per-unit rate into a total cost or a count of tiles or bricks.
- Use volume and a flow rate to find the time to fill or empty a tank.
What is inside this lesson
- 1Mensuration with a real-world wrapper
- 2Paths around and through a field
- 3Cost, tiles and bricks
- 4Tanks and flow rate
- 5Worked example
- 6Common mistakes
- 7Quick revision
- 8Practice
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Mensuration with a real-world wrapper
These questions take a plain area or volume and wrap a context around it: a gravel path around a lawn, a floor to be carpeted at so many rupees per square metre, bricks in a wall, water filling a tank. The geometry is easy; the marks are lost in the wrapper — a wrong base, a double-counted strip, a units slip between the area and the rate.
The method is always the same two steps: find the area or volume that matters, then multiply by the rate or divide by the flow. Keep every length in one unit before you start.
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