# Area Of A Kite Formula

## Area of a Kite Formula

A quadrilateral having reflection symmetry across a diagonal is referred to as a kite in Euclidean geometry. A kite has two equal angles and two pairs of adjacent equal-length sides as a result of its symmetry. Kites are also known as deltoids. The name “deltoids” can also refer to a deltoid curve, an unrelated geometric object occasionally explored in relation to quadrilaterals. If a kite is not convex, it may also be called a dart. The Area Of A Kite Formula is dependent on its shape, which consists of four non-collinear points connected together to form a closed figure with four sides. This shape is a quadrilateral. To put it another way, the Area Of A Kite Formula is the measure of space it encloses or encompasses in a two-dimensional plane. A kite’s four sides are not equal, unlike a square or rhombus. Additionally, the Area Of A Kite Formula is usually expressed in square units. The diagonals of every kite are orthodiagonal (at right angles), and when convex, they are tangential quadrilaterals (their sides are tangent to an inscribed circle). The quadrilaterals that are orthodiagonal and tangential are the convex kites. In addition to the squares, which are special examples of both right kites and rhombi, they also include the right kites, which have two opposite right angles, the rhombi, which have two diagonal axes of symmetry, and the squares.

## Proof

A kite’s area is calculated as half of the product of the lengths of its two diagonals.

Area Of A Kite Formula = 1/2 d1 d2

where,

d1 = the kite’s shorter diagonal

d2 = the kite’s longer diagonal

The definition of a quadrilateral is a form of a polygon with four sides, four vertices, four angles, and two diagonals. The total internal angle of a quadrilateral is 360 degrees. Quadrilaterals take many shapes. The word is a mixture of two Latin words, quadri, which indicates a version of four, and latus, which means side. There are some unique parallelogram types, including rectangles, squares, rhombuses, kites, and more.

### Formula for Area of a Quadrilateral

A kite’s diagonals are perpendicular. The Area Of A Kite Formula is the same as the area of a rhombus. The Area Of A Kite Formula can be used to express the area of a kite.

Area Of A Kite Formula = ½ D1 x D2

where D1 is the kite’s long diagonal and D2 is the short diagonal.

### Properties

Angles between the sides that are not equal are equal.  A pair of congruent triangles having a common base can be thought of as a kite. A kite’s diagonals cross each other at right angles. The shorter diagonal is bisected perpendicularly by the longer diagonal. A kite’s primary diagonal is symmetrical. The kite is split into two isosceles triangles by the shorter diagonal. The sides are split into two pairs, with neighbouring sides in each pair being the same length.  The two vertices joining the uneven sides have identical angles.  A kite’s diagonals meet at a straight angle. The kite’s circumference is equal to twice the sum of its uneven sides.

### Derivation for Area of a Kite

Let ACD and ABD be the two triangles.  Diagonal d2 cuts diagonal d1 in half, therefore the heights of both triangles are equal to (d1)/2.  Triangles ACD and ABD share the same base, which is AD.  As a result, the base length equals the length of AD and d2. The formula for a triangle’s area is

Area of triangle = base × altitude × 1/2.

We can write ABCD for the kite.

Triangle ACD plus triangle ABD equals the area of the kite ABCD.

ABCD = 1/2 d2 (d1)/2 + 1/2 d2 (d1)/2 = 1/2 d2 d1 Area of the kite.

Therefore, we may write

Area Of A Kite Formula ABCD =  1/2 × d1 × d2

### Solved Examples

Solved examples on Area Of A Kite Formula can be found on the Extramarks website and mobile application.