Square and Rectangle

When you say quadrilateral, most people probably first think of a square or a rectangle. The two right-angled figures are seen everywhere.

It is your computer screen, a football field, an A4 sheet of paper, etc.

 

Common to all quadrilaterals is that the angle sum is \(360^\circ\)

 

$$ \Large \angle A + \angle B + \angle C + \angle D = 360^\circ $$

 

Rectangle

A rectangle is a quadrilateral where all angles are 90 degrees. This means that the sides are parallel.

 

Rectangle

 

Square

If all four sides are of equal length, it is called a square. Thus a square is also a rectangle, and therefore the same calculation rules apply.

 

Square

 

Calculation

For a rectangle it is normally necessary to know both sides in order to calculate perimeter and area. Unless it is a square, then one side is enough, since they are equal.

But if you know the diagonal, you can divide the quadrilateral into two right-angled triangles, which gives other possibilities for calculation.

 

 

Rectangle with diagonal

 

If you have learned about equations, you can turn the formulas around and calculate the sides, provided you know area or perimeter.

 

 

Calculator

Formulas

Side a

$$ a=\frac{Areal}{b} $$

$$ a=\sqrt{d^2-b^2} $$

$$ a=\frac{P-(2\cdot b)}{2} $$

Side b

$$ b=\frac{Areal}{a} $$

$$ b=\sqrt{d^2-a^2} $$

$$ b=\frac{P-(2\cdot a)}{2} $$

Diagonal

$$ d=\sqrt{a^2+b^2} $$

Perimeter

$$ P=2a+2b $$

Area

$$ A=a\cdot b $$