The Properties, Formulas, and Examples of Squares in Mathematics

Square

A square is a four-sided polygon with equal sides and four right angles

A square is a four-sided polygon with equal sides and four right angles. It is a special type of rectangle where all sides are equal in length.

Properties of a square:
1. All sides are equal in length.
2. All angles are right angles, measuring 90 degrees.
3. Opposite sides are parallel and congruent.
4. Diagonals bisect each other at 90 degrees.
5. The sum of all interior angles is 360 degrees.
6. The perimeter of a square is obtained by multiplying the length of one side by 4.
7. The area of a square is obtained by squaring the length of one side.

Formulas for a square:
1. Perimeter: P = 4s, where P is the perimeter and s is the length of each side.
2. Area: A = s^2, where A is the area and s is the length of each side.
3. Diagonal: d = s√2, where d is the length of the diagonal and s is the length of each side.

Example:
Let’s say we have a square with a side length of 5 units. We can calculate its perimeter and area:
1. Perimeter: P = 4s = 4 * 5 = 20 units.
2. Area: A = s^2 = 5^2 = 25 square units.
3. Diagonal: d = s√2 = 5√2 ≈ 7.07 units.

So, the perimeter of the square is 20 units, the area is 25 square units, and the length of the diagonal is approximately 7.07 units.

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