Diagonals of a rectangle - Math Open Reference

Diagonals of a rectangle

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. (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

Length of the diagonal

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:
w is the width of the rectangle
h is the height of the rectangle

Things to try

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.

Length of the diagonal

Things to try

Related polygon topics

General

Types of polygon

Area of various polygon types

Perimeter of various polygon types

Angles associated with polygons

Named polygons