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

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

A rectangle has two diagonals. Each one is a line segment drawn between the opposite vertices (corners) of the rectangle. 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 rectangle 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 rectangle into two congruent right triangles. Because the triangles are congruent, they have the same area, and each triangle has half the area of the rectangle

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

As a formula: where:ENTER THE TWO SIDE LENGTHS | ||

Side 1 | clear | |

Side 2 | clear | |

Area: | ||

Perimeter: | ||

Diagonal: | ||

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

Enter the two side lengths and the rest will be calculated. For example, enter the two side lengths. The area, perimeter and diagonal lengths will be found.

- In the figure at the top of the page, click on 'reset' and 'hide details'. Then drag the corners to create an arbitrary rectangle. Calculate the length of the diagonals. Click 'show details' to verify your answer.
- A rectangle has a height of 12 and a diagonal of 31. Find the width of the rectangle and use the animation or the calculator above to verify your answer.

- 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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