Area, Perimeter and Accuracy of Measurement

In short: Area is the space inside a flat shape, measured in square units, so you square the conversion factor: $1{\text{ m}}^2=10000{\text{ cm}}^2$. Every measurement has an absolute error of half its smallest unit, and percentage error is that error divided by the measurement, times 100%.

Starting point: Years 9 and 10

Units

$$1\text{ km}=1000\text{ m}1\text{ m}=100\text{ cm}1\text{ cm}=10\text{ mm}$$

For area, square the conversion:

$$1{\text{ m}}^2=100^2{\text{ cm}}^2=10000{\text{ cm}}^{2}1\text{ ha}=10000{\text{ m}}^{2}1{\text{ km}}^2=1000000{\text{ m}}^2$$

Area formulas

The height $h$ is always measured at right angles to the base.

Composite shapes

Split a shape into simple pieces and add, or take a piece away and subtract.

Accuracy of measuring instruments

No measurement is exact. A measurement is only as accurate as the smallest marking on the instrument.

Relative error and percentage error compare the error with the measurement:

$$\text{relative error}=\frac{\text{absolute error}}{\text{measurement}}\text{percentage error}=\text{relative error}\times 100\%$$

For 8.45 m: $\frac{0.005}{8.45}\times 100\%\approx 0.06\%$.

Quick summary

• Square the conversion factor for area: $1{\text{ m}}^2=10000{\text{ cm}}^2$, $1\text{ ha}=10000{\text{ m}}^2$.
• Know the area formulas for triangles, quadrilaterals, circles and sectors. Height is perpendicular to the base.
• Composite shapes: add the pieces, subtract the holes.
• Absolute error is half the smallest unit. Bounds are the measurement plus and minus it.
• Percentage error $=\frac{\text{absolute error}}{\text{measurement}}\times 100\%$.

Quiz