Area

The square unit is the area of the square which side is the unit length, that is to say the multiplication of unit length by it itself.

The most common units of area are the squares of the length units:

• square millimetres \(\left(\mathrm{mm}^{2}\right)\)
• square centimetres \(\left(\mathrm{cm}^{2}\right)\)
• square metres \(\left(\mathrm{m}^{2}\right)\)
• square kilometres \(\left(\mathrm{km}^{2}\right)\)
• hectares (ha).

onvertir \(1 \mathrm{~cm}^{2}\) en \(\mathrm{~mm}^{2}\)

\(\begin{aligned}&1 \mathrm{~cm}^{2}=10 \mathrm{~mm} \times 10 \mathrm{~mm}=100 \mathrm{~mm}^{2}\\&1 \mathrm{~m}^{2}=100 \mathrm{~cm} \times 100 \mathrm{~cm}=10\,000 \mathrm{~cm}^{2}\\&1 \mathrm{~ha}=100 \mathrm{~m} \times 100 \mathrm{~m}=10\,000 \mathrm{~m}^{2}\\&1 \mathrm{~km}^{2}=1000 \mathrm{~m} \times 1000 \mathrm{~m}=1\,000\,000 \mathrm{~m}^{2} \text { or } 100 \mathrm{ha}\end{aligned}\)

Convert \(10.5\mathrm{~m}^2\) to \(\mathrm{cm}^2\)

• Solution 1:\(\begin{aligned}[t]10.5\mathrm{~m}^2 &=10.5\times 10\,000\mathrm{~cm}^2 \\&=105\,000\mathrm{~cm}^2\end{aligned}\)
• Solution 2:\(10\virgule 5\mathrm{~m}^2 =105\,000\mathrm{~cm}^2\)

The area of a figure is the number of square units it contains.

Find the area of the red figure :

Name	Shape	Area
Rectangle		\( A= l \times w \)
Square		\(\begin{aligned} A&= l^2\end{aligned}\)
Parallelogram		\( A= b\times h\)
Triangle		\(A=\dfrac{b\times h}{2}\)
Circle		\(A=\pi r^2\)
Trapezium		\( A= \dfrac{a+b}{2}\times h\)

A composite figure is made up of simple geometric shapes.

To find the area of a composite figure,

1. divide it into simple, nonoverlapping figures
2. find the area of each simpler figure
3. add the areas together to find the total area of the composite figure