Rules for Squares in Algebra

Perimeter

• The perimeter of a square is the total distance around the exterior of the shape. In more complex shapes, such as a trapezoid, this would be achieved by adding each of the four sides together. But since squares have four equal sides, the formula Perimeter = 4x applies. For example, in a square with sides measuring 3, Perimeter = 4 * 3 = 12.

Area

• The area of a square is the total amount of space the square covers. The formula for area is the multiplication of two sides, or Area = x * x = x^2. For example, in a square with sides measuring 5, Area = 5 * 5 = 25.

Angles

• Because all four of the sides are equal, or congruent, the four angles in a square each measure 90 degrees; 90-degree angles are also called right angles. Furthermore, two diagonals can be drawn through a square, which creates four equal right triangles with interior angle measurements of 90 degrees.

Diagonal

• The formula for calculating a single diagonal of a square is the length of the side multiplied by the square root of 2, which could be written Diagonal = x√2. This is because the diagonal creates two equal right triangles with the diagonal serving as the hypotenuse. The Pythagorean theorem, which applies to right triangles, states that a^2 + b^2 = c^2 where "a" and "b" are sides (in this case, sides of the square) and "c" is the hypotenuse (in this case, the diagonal).

  For example, in a square with sides measuring 5, the Pythagorean theorem would read 5^2 + 5^2 = c^2 or 25 + 25 = c^2 or 50 = c^2. Take the square root of both sides: c = √50 = 7.07 (rounded). Check that this equals the diagonal formula: Diagonal = 5 * √2 = 7.07 (rounded).