Area Of A Kite - Formula, Definition, Examples - Cuemath

Area of Kite

Area of kite is the space enclosed by a kite. A kite is a quadrilateral in which two pairs of adjacent sides are equal. The elements of a kite are its 4 angles, its 4 sides, and 2 diagonals. In this article, we will focus on the area of a kite and its formula.

1.	What is the Area of a Kite?
2.	Area of a Kite Formula
3.	Derivation of the Area of Kite Formula
4.	FAQ's on Area of a Kite

What is the Area of a Kite?

The area of a kite can be defined as the amount of space enclosed or encompassed by a kite in a two-dimensional plane. Like a square, and a rhombus, a kite does not have all four sides equal. The area of a kite is always expressed in terms of units2 for example, in2, cm2, m2, etc. Let us learn about the area of a kite formula in our next section.

Area of a Kite Formula

The area of a kite is half the product of the lengths of its diagonals. The formula to determine the area of a kite is: Area = ½ × (d)1 × (d)2. Here (d)1 and (d)2 are long and short diagonals of a kite. The area of kite ABCD given below is ½ × AC × BD.

BD = Long diagonal and AC = Short diagonal

Derivation of the Area of Kite Formula

Consider a kite ABCD as shown above.

Assume the lengths of the diagonals of ABCD to be AC = p, BD = q

We know that the longer diagonal of a kite bisects the shorter diagonal at right angles, i.e., BD bisects AC and ∠AOB = 90°, ∠BOC = 90°.

Therefore,

AO = OC = AC/2 = p/2

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

We know that,

Area of a triangle = ½ × Base × Height

Now, we will calculate the areas of triangles ABD and BCD

Area of ΔABD = ½ × AO × BD = ½ × p/2 × q = (pq)/4

Area of ΔBCD = ½ × OC × BD = ½ × p/2 × q = (pq)/4

Therefore, using (1)

Area of kite ABCD = (pq)/4 + (pq)/4 = (pq)/2 Substituting the values of p and q Area of a kite = ½ × AC × BD

Important Notes

• The perimeter of a kite is \(2(Side_1 + Side_2)\)
• The area of a kite is ½ × (d)1 × (d)2
• A kite has two pairs of adjacent equal sides.
• A kite is a cyclic quadrilateral, hence, satisfies all the properties of a cyclic quadrilateral.