Definition: A quadrilateral with two distinct pairs of equal adjacent sides.
A kite-shaped figure.
Try this Drag the orange dots on each vertex to reshape the kite. Notice how
always equals

Image courtesy Nothridge Schools
A kite is a member of the quadrilateral family, and while easy to understand visually, is a little tricky to define in precise mathematical terms. It has two pairs of equal sides. Each pair must be adjacent sides (sharing a common vertex) and each pair must be distinct. That is, the pairs cannot have a side in common.

Drag all the orange dots in the kite above, to develop an intuitive understanding of a kite without needing the precise 'legal' definition.

Properties of a kite

  • Diagonals intersect at right angles.
    In the figure above, click 'show diagonals' and reshape the kite. As you reshape the kite, notice the diagonals always intersect each other at 90° (For concave kites, a diagonal may need to be extended to the point of intersection.)

  • Angles between unequal sides are equal
    In the figure above notice that ABC = ADC no matter how how you reshape the kite.

  • Area
    The area of a kite can be calculated in various ways. See Area of a Kite

  • Perimeter
    The distance around the kite. The sum of its sides. See Perimeter of a Kite

  • A kite can become a rhombus
    In the special case where all 4 sides are the same length, the kite satisfies the definition of a rhombus. A rhombus in turn can become a square if its interior angles are 90°. Adjust the kite above and try to create a square.

Concave kites

If either of the end (unequal) angles is greater than 180°, the kite becomes concave. Although it no longer looks like a kite, it still satisfies all the properties of a kite. This shape is sometimes called a dart. To see this, in the figure above drag point A to the right until is passes B.

Related polygon topics


Types of polygon

Area of various polygon types

Perimeter of various polygon types

Angles associated with polygons

Named polygons