All About Squares: Properties, Formulas, and Measurements

Square

A square is a geometric shape that has four equal sides and four equal angles of 90 degrees each

A square is a geometric shape that has four equal sides and four equal angles of 90 degrees each. It is a special type of rectangle where all sides are congruent.

Properties of a Square:
1. All sides are equal in length: The length of all four sides are the same, which makes them congruent.
2. All angles are equal: Each angle in a square is 90 degrees. The sum of all angles in a square is 360 degrees.
3. Opposite sides are parallel: The opposite sides of a square are parallel to each other.
4. Diagonals are equal and bisect each other: The diagonals of a square are equal in length and intersect at 90 degrees, bisecting each other.
5. Diagonals form right-angled triangles: The diagonals of a square divide it into four right-angled triangles.

Formulas and measurements for a Square:
1. Perimeter: Perimeter is the sum of the lengths of all the sides of a square. For a square, the formula for perimeter is P = 4s, where “s” represents the length of one side.
2. Area: The area of a square is found by multiplying the length of one side by itself. The formula for the area of a square is A = s^2, where “s” represents the length of one side.
3. Diagonal length: The diagonal length of a square can be found using the Pythagorean theorem. With “s” as the length of one side of the square, the formula for the length of the diagonal is D = s√2.

Example:
Let’s say we have a square with a side length of 6 cm.

To find the perimeter, we use the formula P = 4s. Substituting the value of s, we get P = 4 * 6 = 24 cm. So, the perimeter of the square is 24 cm.

To find the area, we use the formula A = s^2. Substituting the value of s, we get A = 6^2 = 36 cm^2. So, the area of the square is 36 square cm.

To find the length of the diagonal, we use the formula D = s√2. Substituting the value of s, we get D = 6√2 ≈ 8.49 cm. So, the length of the diagonal is approximately 8.49 cm.

I hope this helps! Let me know if you have any more questions.

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