Properties and Formulas of Squares in Mathematics: Perimeter, Area, and Diagonal Calculation

Square

A square is a four-sided polygon with four equal sides and four equal angles of 90 degrees each

A square is a four-sided polygon with four equal sides and four equal angles of 90 degrees each. It is a special type of rectangle where all sides are equal in length.

Properties of Square:
1. All four sides are equal in length.
2. All four angles are right angles (90 degrees).
3. Opposite sides are parallel and congruent.
4. Opposite angles are congruent.
5. Diagonals bisect each other at 90 degrees.
6. The sum of interior angles of a square is always 360 degrees.

Formulas related to Square:
1. Perimeter: The perimeter of a square is calculated by adding the lengths of all four sides. It can be represented as P = 4s, where s is the length of any side.
2. Area: The area of a square is calculated by squaring the length of one side, which can be represented as A = s^2, where s is the length of any side.
3. Diagonal: The length of the diagonal of a square can be found using the Pythagorean theorem, which states that the square of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides. It can be represented as d = s√2, where d is the length of the diagonal and s is the length of any side.

Example:
Let’s say we have a square with a side length of 5 units. We can find its perimeter, area, and diagonal length using the formulas mentioned above.

1. Perimeter: P = 4s = 4 * 5 = 20 units
So, the perimeter of the square is 20 units.

2. Area: A = s^2 = 5^2 = 25 square units
So, the area of the square is 25 square units.

3. Diagonal: d = s√2 = 5 * √2 ≈ 7.071 units (rounded to three decimal places)
So, the length of the diagonal of the square is approximately 7.071 units.

I hope this explanation helps you understand the concept of squares and how to calculate their perimeter, area, and diagonal length.

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