A
square
has two diagonals, which are
line segments
linking opposite
vertices (corners) of the square.

Try this
Drag any vertex of the square below. It will remain a square and the length of the diagonal will be calculated.

A square has two diagonals. Each one is a line segment drawn between the opposite vertices (corners) of the square. The diagonals have the following properties:

- The two diagonals are congruent (same length). In the figure above, click 'show both diagonals', then drag the orange dot at any vertex of the square and convince yourself this is so.
- Each diagonal bisects the other. In other words, the point where the diagonals intersect (cross), divides each diagonal into two equal parts
- Each diagonal divides the square into two congruent isosceles right triangles. Because the triangles are congruent, they have the same area, and each triangle has half the area of the square.

In the figure above, click 'reset'. As you can see, a diagonal of a square divides it into two right triangles, BCD and DAB. The diagonal of the square is the hypotenuse of these triangles. We can use Pythagoras' Theorem to find the length of the diagonal if we know the side length of the square.

As a formula: wherewhich simplifies to:

ENTER ANY ONE VALUE | ||

Side | clear | |

Perimeter | clear | |

Area | clear | |

Diagonal | clear | |

Use the calculator above to calculate the properties of a square.

Enter any one value and the other three will be calculated. For example, enter the side length and the diagonal will be calculated.

Similarly, if you enter the area, the side length needed to get that area will be calculated.

- Polygon general definition
- Quadrilateral
- Regular polygon
- Irregular polygon
- Convex polygons
- Concave polygons
- Polygon diagonals
- Polygon triangles
- Apothem of a regular polygon
- Polygon center
- Radius of a regular polygon
- Incircle of a regular polygon
- Incenter of a regular polygon
- Circumcircle of a polygon
- Parallelogram inscribed in a quadrilateral

- Square
- Diagonals of a square
- Rectangle
- Diagonals of a rectangle
- Golden rectangle
- Parallelogram
- Rhombus
- Trapezoid
- Trapezoid median
- Trapezium
- Kite
- Inscribed (cyclic) quadrilateral

- Regular polygon area
- Irregular polygon area
- Rhombus area
- Kite area
- Rectangle area
- Area of a square
- Trapezoid area
- Parallelogram area

- Perimeter of a polygon (regular and irregular)
- Perimeter of a triangle
- Perimeter of a rectangle
- Perimeter of a square
- Perimeter of a parallelogram
- Perimeter of a rhombus
- Perimeter of a trapezoid
- Perimeter of a kite

- Exterior angles of a polygon
- Interior angles of a polygon
- Relationship of interior/exterior angles
- Polygon central angle

- Tetragon, 4 sides
- Pentagon, 5 sides
- Hexagon, 6 sides
- Heptagon, 7 sides
- Octagon, 8 sides
- Nonagon Enneagon, 9 sides
- Decagon, 10 sides
- Undecagon, 11 sides
- Dodecagon, 12 sides

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