Square Calculator
What is a Square?
A square is a four-sided polygon (quadrilateral) with all sides of equal length and all angles equal to 90 degrees.
Key Properties of Squares
- All sides are equal in length
- All angles are right angles (90 degrees)
- Diagonals bisect each other at right angles
- Diagonals are equal in length
Formulas for Squares
Let \(s\) be the length of a side. Then:
- Area: \(A = s^2\)
- Perimeter: \(P = 4s\)
- Diagonal: \(d = s\sqrt{2}\)
Step-by-Step Calculations
Let's calculate these properties for a square with side \(s = 5\) units:
- Area:
\[A = s^2 = 5^2 = 25 \text{ square units}\]
- Perimeter:
\[P = 4s = 4(5) = 20 \text{ units}\]
- Diagonal:
\[d = s\sqrt{2} = 5\sqrt{2} \approx 7.07 \text{ units}\]
Visual Representation
This diagram illustrates the square with the calculated dimensions and properties.