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# Formulas and Tables

Elementary Geometry

# Square

Side of a square: $$a$$
Diagonal of a square: $$d$$
Radius of the circumscribed circle: $$R$$
Radius of the inscribed circle: $$r$$

Perimeter: $$P$$
Area: $$S$$

1. A square is a regular quadrilateral. It has four equal sides and four equal angles ($$90^\circ$$ angles).
1. Diagonal of a square
$$d = a\sqrt 2$$
2. Radius of the circumscribed circle
$$R = d/2 =$$ $$a\sqrt 2/2$$
3. Radius of the inscribed circle
$$r = a/2$$
4. Perimeter of a square
$$P = 4a$$
5. Area of a square
$$S = {a^2} = {\large\frac{{{d^2}}}{2}\normalsize} =$$ $$2{R^2} = 4{r^2}$$