Example 1
\(s = 6 \rightarrow A = 6^2 = 36\) units², \(P = 4 \times 6 = 24\) units, \(d = 6\sqrt{2} \approx 8.49\) units
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Theory & Formula
A square is a regular quadrilateral with four equal sides and four right angles. It is a special case of a rectangle where length equals width.
The diagonal of a square divides it into two congruent right triangles and can be calculated using the Pythagorean theorem: d² = s² + s² = 2s², so d = s√2.
Properties
- All four sides are equal
- All four angles are 90 degrees
- Diagonals are equal, bisect each other at 90 degrees
- Diagonals divide the square into 4 congruent isosceles right triangles
- Has 4 lines of symmetry and rotational symmetry of order 4
\(A = s^2, P = 4s, d = s\sqrt{2}\)
Worked Examples
Example 2
\(s = 10 \rightarrow A = 10^2 = 100\) units², \(P = 4 \times 10 = 40\) units, \(d = 10\sqrt{2} \approx 14.14\) units