What are the Mathematical Properties of a Kite?
A kite is a 4 sided shape (quadrilateral) and has the following properties:
A kite has two pairs of equal side lengths. So in the diagram pictured sides AD and AB are equal, and sides DC and BC are equal in length.
A kite also has one pair of equal angles. In the diagram pictured angles D and B are equal.
A kite has exactly one line of reflectional symmetry. The line of symmetry will be AC in the diagram shown.
A kite doesn’t have rotational symmetry. This means you cannot rotate the shape onto itself in a full turn. Therefore, the order of rotational symmetry of a kite is order 1.
If you draw the diagonals of a kite as shown in the diagram then the diagonals will bisect each other at right angles.
The area of the kite can be worked out by multiplying the lengths of the diagonals and dividing this answer by 2. So in the diagram shown the formula for working out the area of a kite will be ½.DB.AC.
Let’s take a look at an example of working out the area of a kite.
Area Of A Kite Example
A kite has diagonal lengths of 8cm and 12cm. Work out the area of this kite.
Remember that all you need to do is multiply the two diagonal lengths together and divide the answer by 2:
8 x 12 = 96 cm2
Now divide this answer by 2:
96/2 = 48 cm2
So the area of this kite is 48 cm2.
So to summarise, the properties of a kite are; 2 pairs of equal side lengths, one pair of equal angles, one line of reflectional symmetry, no rotational symmetry (order 1) and the area of a kite can be found by multiplying the diagonal side lengths and dividing this answer by 2.