Square (Geometry)

(Jump to Area of a Square or Perimeter of a Square)

A Square is a flat shape with 4 equal sides and every angle is a right angle (90°)

Square    
quadrilateral right-angle key means "right angle"
quadrilateral equal key show equal sides
 
right arrow All sides are equal in length
right arrow Each internal angle is 90°
right arrow Opposite sides are parallel (so it is a Parallelogram).

Play with a square:

A square also fits the definition of a rectangle (all angles are 90°), and a rhombus (all sides are equal length).

Area of a Square

square  

The Area is the side length squared:

Area = a2 = a × a

Example: A square has a side length of 6 m, what is its Area?

Area = 6 m × 6 m = 36 m2

square diagonal   The Area is also half of the diagonal squared:

Area = d2/2

Perimeter of a Square

The Perimeter is the distance around the edge.

square perimeter  

The Perimeter is 4 times the side length:

Perimeter = 4a

Example: A square has a side length of 12 cm, what is its Perimeter?

Perimeter = 4 × 12 cm = 48 cm

Diagonals of a Square

A square has two diagonals, they are equal in length and intersect in the middle.

square diagonal  

The Diagonal is the side length times the square root of 2:

Diagonal "d" = a × √2

Example: A square has a side length of 5 m, what is the length of a diagonal?

square diagonal example Diagonal Length = a × √2 = 5 × 1.41421... = 7.071 m (to 3 decimals)