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QUADRILATERAL

Quadrilateral > Kite

KITE

Definition

A kite is a quadrilateral that has TWO (2) PAIRS OF EQUAL ADJACENT SIDES THAT ARE EQUAL IN LENGTH.

A drawing showing a kite that has two pairs of equal ADJACENT sides that are equal in length.

INTERESTING FACTS:

When all sides have equal length, the kite will also be a rhombus.
When all angles are right angles (90°), the kite will also be a square.
A kite sometimes looks like an old fashion kite. Hence, a familiar term is a “box kite.”

It Is Helpful To Think

It is helpful to think of a KITE as a RECTANGLE or SQUARE with its four (4) edges folded into a shape of a kite, a diamond (rhombus) or a box (square).

A box kite is a high performance kite, noted for developing relatively high lift; it is a type within the family of cellular kites. The typical design has four parallel struts. The box is made rigid with diagonal crossed struts. (Wikipedia)

Sides are said to be adjacent when they share a common endpoint.

A drawing showing showing a rectangle with it four edges folded inward creating a shape of a kite.

Traditional Formula

Area_Kite = (d₁ x d₂)/2

A drawing showing a kite with two diagonals in it.

NOTES:

DIAGONALS are lines (dashed) that cross at right angles and one of the diagonals bisects (cuts equally in half) the other.
Angles are equal where two pairs meet.

Thinking Inside The Box

If you place a KITE inside of a box (a rectangle or a square) and fold the right or left side that are separated by a diagonal into the opposite side, you will get a rectangle or square that is half of the box that it is in.

A drawing showing a kite with the right side that are separated by diagonals being rotated to the other side creating a smaller rectangle.

When all sides have equal length, the kite will also be a rhombus or a square.

NOTE: Note also that you could had folded the top or bottom instead of the left or right side of this kite.

KEY: Hence, you can use the rectangle formula instead of the kite formula to derive its area. Since a kite is thought of as a special rectangle or square , you can multiple the two diagonals together as though they were the height and width of a rectangle and divide it by two to get its area.

ExampleS

A kite with diagonals of 4 in and 7 in has an area of:

Treat the two diagonals as the height and width of a rectangle.
Use the rectangle formula instead (Area_Kite = height x width).
Divide the result by 2.

Area_Kite = (4 in × 7 in)/2 = 28 in/2 = 14 in²

A kite with both diagonals of 4 in has an area of:

Treat the two diagonals as the height and width of a rectangle.
Use the rectangle formula instead (Area_Kite = height x width).
Divide the result by 2.

Area_Kite = (4 in × 4 in)/2 = 16 in/2 = 8 in²

REFERENCE: See screenshots above for graphic representations.

Memorization Tip

To remember the similarities between a kite and a triangle, it is helpful to think of a KITE or a TRIANGLE as HALF of a rectangle or a square. Hence, you divide the result by two.