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
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
the other. In other words, the point where the diagonals
divides each diagonal into two equal parts
- Each diagonal divides the square into two
Because the triangles are congruent, they have the same
area, and each triangle has half the area of the square.
Length of the diagonal
In the figure above, click 'reset'. As you can see, a diagonal of a square divides it into two
BCD and DAB.
The diagonal of the square is the
of these triangles.
We can use
to find the length of the diagonal if we know the side length of the square.
As a formula:
which simplifies to:
s is the length of any side
If you know the
of a square, you can calculate all the other properties, including the diagonal lengths.
For more on this, see
Square (Coordinate geometry)
Things to try
In the figure at the top of the page, click on 'reset' and 'hide details'.
Then drag any corner to create an arbitrary square.
Calculate the length of the diagonals.
Click 'show details' to verify your answer.
Related polygon topics
Types of polygon
Area of various polygon types
Perimeter of various polygon types
Angles associated with polygons
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