## Area of a kite formula

The types of polygons that have four sides, four vertices, and four angles along with a pair of diagonals are referred to as quadrilaterals. There are some special types of parallelograms like rectangle, square, rhombus, kite, etc.

A special quadrilateral in which each pair of consecutive sides is congruent, but the opposite sides are not congruent is called a kite. Angles between unequal sides are equal.

The kite can be represented as a pair of congruent triangles with a common base.

The diagonals of a kite intersect each other at right angles.

The longer diagonal is said to be the perpendicular bisector of the shorter diagonal.

## Derivation

BD = Long diagonal and AC = Short diagonal

The Figure given below,

Derivation of Area of the Kite

Let,

the long diagonal BD = d_{1}

the short diagonal AC = d_{2},

AC = AO + OC = d_{2}

Area of kite ABCD = Area of ΔABD + Area of ΔBCD… (1)

We know that,

Triangle’s Area = ½ × Base × Height

Now, let us calculate the areas of triangles ABD and BCD

Area of ΔABD = ½ × AO × BD = ½ × AO × d_{1}

Area of ΔBCD = ½ × OC × BD = ½ × OC × d_{1}

Therefore, by using (1),

Area of kite ABCD = ΔABD + ΔBCD

That is

ΔABCD= ½ × AO × d_{1} + ½ × OC × d_{1}

= ½× d_{1} x (AO + OC)

= ½ × d_{1} x d_{2}

Therefore, Δ ABCD = ½ × d_{1} x d_{2}

Thus, we need to just multiply both the diagonal values and divide them by 2, when both diagonal values are given, to get the area of the kite.

## Let us take some examples of the Area of kite formula

**1) A kite with an area of 126 cm ^{2} has one of its diagonals that is 21cm long. Find the length of the other diagonal.**

**Solution:** Given,

Area of a kite =126 cm^{2}

Length of one diagonal = 21 cm

Area of Kite =

D_{2} = 12cm

**2) Given the larger diagonal, it is twice the smaller diagonal.**

**What is the relation between the area and the smaller diagonal of a kite?**

**Solution:**

Let us assume that

the smaller and larger diagonal be d and 2d respectively.

Consider the area of the kite to be A.

Thus, we can write as

A = 1/2 × d × (2d)

A = d^{2}

Thus, the area of the kite is the square of the smaller diagonal.