Understanding the Properties and Formulas of Squares in Mathematics

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In mathematics, a square is a geometrical figure that has four equal sides and four equal angles

In mathematics, a square is a geometrical figure that has four equal sides and four equal angles. It is a special type of quadrilateral, or four-sided polygon.

Properties of a square:

1. Sides: All four sides of a square are of equal length, which means that the perimeter of a square is equal to four times the length of one side.

2. Angles: Each interior angle of a square measures 90 degrees, making it a right angle. Additionally, the four angles of a square are congruent, or equal in measure.

3. Diagonals: The diagonals of a square are perpendicular and bisect each other. This means that the diagonals intersect at a 90-degree angle, and each diagonal divides the square into two congruent right triangles.

4. Symmetry: A square possesses rotational symmetry of order 4. This means that it looks the same after rotation by 90, 180, and 270 degrees.

Formulas related to squares:

1. Area: The area of a square is calculated by multiplying the length of one side by itself. So, the formula for the area of a square is A = s^2, where A represents the area and s represents the side length.

2. Perimeter: As mentioned earlier, the perimeter of a square is equal to four times the length of one side. Therefore, the formula to find the perimeter, P, of a square is P = 4s, where s represents the side length.

Example: Let’s say we have a square with a side length of 5 units. To find the area, we can use the formula A = s^2, which becomes A = 5^2 = 25 square units. To find the perimeter, we can use the formula P = 4s, which becomes P = 4(5) = 20 units.

In summary, a square is a polygon with four equal sides and four congruent 90-degree angles. It possesses properties like equal sides, congruent angles, perpendicular diagonals, and rotational symmetry. The area of a square is calculated by squaring the side length, while the perimeter is found by multiplying the side length by 4.

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