Area of a square
Area A = a x a = a2

A side of the square = a
AB = BC = CD = DA

Example

ABCD is a square with side a = 4 cm
Area A of the square ABCD = a x a = 4 x 4 = 16 cm²

Calculate the area of a square

Side a
Area of the square

Square

A square is a geometric shape with four equal sides, four right angles, and sides meeting at 90-degree angles. Its area is calculated by multiplying the length of one side by itself.

A square is a polygon characterized by four congruent sides and four right angles. Each interior angle measures 90 degrees. Its properties include symmetry, equal diagonals, and a calculated area obtained by squaring the length of one side. In Euclidean geometry, a fundamental shape with practical applications in mathematics and various fields.

Properties of a square

Equal sides: all four sides of a square are of equal length.

Right angles: each interior angle measures 90 degrees, forming right angles.

Congruent diagonals: the diagonals bisect each other at right angles and are of equal length.

Symmetry: a square exhibits symmetry with respect to its center and each of its sides.

Diagonal properties: diagonals are equal in length, and the square can be divided into four congruent right-angled triangles.

Perimeter: the perimeter of a square is four times the length of one side.

Area formula: the area is calculated as the square of the length of one side.

Vertex angles: all four vertex angles are right angles.

Interior angles: the sum of interior angles is always 360 degrees.

Regular polygon: a square is a regular polygon, meeting criteria for both equilateral and equiangular properties.

Inscribed circle: a square has a unique property where a circle can be inscribed within it, touching the midpoint of each side.

Circumcircle: the center of the square is also the center of the circumcircle (the circle passing through all four vertices).

Angle bisector: the diagonals of a square bisect each other's angles, creating congruent adjacent angles.

Equal opposite angles: opposite angles in a square are equal.

Orthodiagonal: the diagonals are orthodiagonal, meaning they intersect at right angles.

Examples

The area (A) of a square can be calculated using the formula:
A = (side length)2

Side length = 5 units:

A = 52 = 25 units2

Side length = 8.2 meters:

A = 8.22 = 67.24 m2

Side length = 12 inches:

A = 122 = 144 in2

Side length = 2.5 centimeters:

A = 2.52 = 6.25 cm2

Side length = 10 feet:

A = 102 = 100 ft2