# Geometry for Elementary School/Measurements

In this chapter, we will talk about something that may seem boring to many but is very useful: measurements. You may have learnt them in science, but here they are anyway. This chapter has no corresponding material in Euclid's *Elements*, and will only serve as a reference chapter.

## Measuring length[edit]

When measuring length, simply put get a ruler and place the '0' on the endpoint of the segment you wish to measure. Then move the ruler so that the edge of the ruler fits the line exactly. Read the marking on the ruler on the other endpoint. That is the length of the ruler.

Some people use the metric system when measuring lengths. That means they use centimetres, millimetres, metres and kilometres. Others use inches, feet and yards. Most people prefer to use the metric system, although many people still use other measuring units.

Sometimes we need to measure a longer distance. Then we can use the tape measure, the trundle wheel, or the metre rule. We will not talk about them in detail here.

Sometimes we need to know the area of the figure. That has been discussed before. If you do not remember that, take a look at the chapter about plane figures. When we calculate the area of the figure, we use only one unit. Let us use centimetres as an example. If a square is 4cm long, then its area is 4cm^{2} which is equal to 16 squared centimetres, or cm^{2}.

## Measuring angles[edit]

Sometimes we need to measure angles. That is, how wide an angle is open. The size of the arms is insignificant. If you remember from the chapter about angles, angles are measured in degrees. So, how can we find out the number of degrees an angle has?

You probably have a measuring tool called a protractor. It looks like a semi-circle with markings along the circumference. Some protractors are full circles. You can use both for measuring angles. To measure an angle, look for a tinky marking at the midpoint of the diameter of the circle. Place that on the vertex of the angle. Now let one of the arms fit the radius exactly. Read the marking on the other arm. That is the size of the angle!

When dealing with reflex angles, a full circle protractor may be better for the purpose, but let's stick to using a half-circle for now. Recall that angles with the same vertice and which add up to 360° are called angles at a point. Notice that in reflex∠ABC, for example, you can also measure ∠ABC. Then you can take ∠ABC away from 360°. That is the size of reflex∠ABC.

## Measuring volume[edit]

Measuring volume may require more complicated apparatus than measuring angles or lengths. In the laboratory, we use measuring cylinders, but since we are not in the laboratory, we usually use beakers instead. However, sometimes we use displacement cans, which are like large beakers with an opening. We can easily find the volume by looking at the water displaced. The concept is discovered by a mathematician called Archimedes.

When measuring volume, we can use the units cm^{3} and m^{3}. For example, if a book is 10cm long, 5cm wide and 1cm thick, its volume would be 50cm^{3}.

A related concept is capacity. Capacity is the amount of liquid that a container can hold. We can use the units, litres and millilitres. For example, a box of vita-soy milk contains about 250 millilitres of soy milk.