Square:Its Properties and Formulas

Properties of square

1. Each angle of a square is a right angle, $\angle A=90{}^\circ ,\angle B=90{}^\circ ,\angle C=90{}^\circ =\angle D=90$.
2. All the sides of a square are equal; AB = BC = CD = DA.
3. Opposite sides are parallel; AB || CD & AD || BC.
4. The diagonals of a square are equal and perpendicular to each other; AC = BD, AC$\bot $ BD.

Formulas of a Square

If Side of square = a

$\begin{align}
& (i)Perimeter=4\times a \\

& (ii)Area=a\times a \\

\end{align}$

(iii) Side of Square = $\sqrt{Area}$

$\begin{align}
& (iv)Diagonal=\sqrt{2}a \\

& (v)Area=\frac{1}{2}{{(Diagonal)}^{2}} \\
\end{align}$

     
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