# SI Length

The base unit of **length** in the Système Internationale d'unités(SI) is the **meter**. The meter has had many definitions but the current official definition is related to the speed of light.

MetreThe distance travelled by light in $\frac{1}{299,792,458} \text{seconds}.$

This may seem like a very arbitrary distance to pick, especially since it is so close to 300,000,000, one might wonder, why not just round up a bit?

But there is a long history behind this exact distance.

At first it was defined as $\frac{1}{10,000,000}$ of the distance from the north pole to the equator. However, this distance being difficult to measure, and perhaps not even constant, a more definitive measurement was sought after. In 1960, the agreed upon definition was based on the wavelength of krypton-86 radiation. This lasted until 1983, when the meter was officially defined as "the length of the path traveled by light in vacuum during a time interval of $\frac{1}{299,792,458}$ of a second", the fraction chosen to match as closely as possible with our previous definition. As this distance is based off the speed of light which has been shown to be a measurable and well defined universal constant, this is likely to remain the definition for quite some time.

## Perimeter

The distance around a 2-dimensional shape is called it's **perimeter**. It can also be defined as the sum of all the side lengths of a 2-dimensional shape. As perimeter is classified as a distance, the unit is the **meter**.

A regular pentagon has a side of length $2\text{ m}.$ What is the perimeter of the figure?

"Regular" means all the side lengths are the same. As a pentagon has five sides, the perimeter is

$\text{Perimeter} = 5\times\text{(side length)} = 5(2\text{ m}) = 10\text{ m}.$

## Area

The **area** is the space enclosed by the edges of a 2-dimensional figure. As it is found by multiplying length by length, area is measured in square units, $\text{units}^2.$ The SI unit of area is meters-squared or $\text{m}^{2}.$

If a Rubik's cube's side length is taken to be $2 \text{ units},$ what is the total surface area of the cube?

Surface areais the total area of all the 2-dimensional sides of a 3-dimensional figure. First, the area of one side of the cube is $\text{Area}_{square}=\text{(side length)}^2 = (2\text{ units})^2 = 4 \text{ units}^2.$Since there are six of these square sides on a cube, the total surface area is $\text{Surface area} = \Sigma\text{(face area)} = 6\times\text{(face area)} = 6(4 \text{ units}^2) = 24\text{ units}^2.$

## Volume

**Volume** is the total space occupied by a 3-dimensional figure. As it is obtained by multiplying three distances together, volume is measured in cubic units. The SI unit of volume is meters-cubed or $m^{3}$.
All objects in real life possess volume.

Volume is most integral to studies of fluids.