Shop prices and GST

Percentage changes in area Area depends on two length measurements. When two lengths in the area formula change, multiply their individual factors to obtain the area factor. For a square, both factors are equal. For a triangle, the constant 12 is unchanged. For a circle, the area pi r2 has the radius factor twice, while the circumference 2pi r has it once. Example For a rectangle of sides L and W, the original area is LW. A 20% increase in length and a 20% decrease in width give New area=(1.20L)(0.80W) =0.96LW. The new area is 96% of the original, a 4% decrease. Check that the factors apply to the lengths before multiplying. Adding the two rates would miss the effect on the area.

Area depends on two length measurements. When two lengths in the area formula change, multiply their individual factors to obtain the area factor. For a square, both factors are equal. For a triangle, the constant \(\tfrac12\) is unchanged. For a circle, the area \(\pi r^2\) has the radius factor twice, while the circumference \(2\pi r\) has it once.

For a rectangle of sides \(L\) and \(W\), the original area is \(LW\). A 20% increase in length and a 20% decrease in width give

\(\begin{aligned}\text{New area}&=(1.20L)(0.80W)\\&=0.96LW\end{aligned}\).

The new area is 96% of the original, a 4% decrease. Check that the factors apply to the lengths before multiplying. Adding the two rates would miss the effect on the area.