## Perimeters, Areas and Volumes

Start off by referring to Key Skills - Formulas

and

### Hectares

A hectare is an area of 10,000m^{2}

If it was as square it would have sides of 100m.

The previous statement is consistent with the idae that the area of a square or rectangle is just one side multiplied by the other. This is straight forward enough, but **be absolutely certain that all sides to be multiplied are in the same units.**

This calculation of area generalizes to cubes or cuboids, e.g. the volume of a cardboard box containing a TV set is just the lengths of the three sides multiplied together ** just so long as all the lengths are given in the same units**, e.g. all in centimeters or all in meters.

At GCSE level, this definition of volume generalizes into finding the volumes of compliocated shapes which nevertheless have constant cross-sections.

Going back to the square hectare, let's consider how many will fit into a square kilometer. Along one side of the square kilometer, ten hectares will fit exactly - and likewise for the other side of the square kilometer. Therefore 100 hectares will fit into a square kilometer, using the same logic that tells you there are 64 squares on a chess board because there are 8 squares along one side and eight squares along the other, giving a total number of squares of 8 x 8 = 64.

### "Packing"

**How many light bulbs can fit completely into the larger carton?**

Pack the light bulb boxes in the same orientation shown in the diagram

Along a side of 40cm, five bulb boxes can be packed completely

Along a side of 60cm, six bulb boxes can be packed completely.

So total number of bulb boxes that can be packed is

5 x 5 x 6 = 150