Area of a Kite

The area of a kite is the total space enclosed by it. The area is expressed in square units such as cm², in², m²,  ft², yd², etc. This article will precisely help you find the area of a kite.

Formula

The basic formula to find the area of a kite is given below:

Using Diagonals

Area (A) = (d₁ × d₂)/2, here d₁ and d₂ are the diagonals

Derivation

Let us derive and prove the above formula for the area of a kite.

In kite ABCD, diagonals AC = d₁, and BD = d₂

So, OB = OD = d2/2

Now, area of kite ABCD = Area of ΔABC + ΔADC

As we know,

Area of a triangle = 1/2 × base × height

In ΔABC, base = AC, height = OB

∴ Area of ΔABC = 1/2 × AC × OB, here AC = d₁, OB = d₂/2

= 1/2 × d₁ × d₂/2

= 1/4 × d₁ × d₂

In ΔADC, base = AC, height = OD

∴ Area of ΔADC = 1/2 × AC × OD, here AC = d₁, OD = d₂/2

= 1/2 × d₁ × d₂/2

= 1/4 × d₁ × d₂

As we know,

Area of kite ABCD = Area of ΔABC + ΔADC

= (1/4 × d₁ × d₂) + (1/4 × d₁ × d₂)

= (d₁ × d₂)/2

So the above derivation is the proof  of area of a kite as 1/2 × d₁ × d₂

Let us solve an example to understand the concept better.

Without Diagonals

The formula to find the area of a kite without diagonals is given below:

Formula:

Area (A) = a × b × sin(θ) here, a and b are 2 adjacent sides, θ = angle between 2 adjacent sides

In Kite (symbol) ABCD, a = AB, b = BC, θ = ∠ABC

Let us solve an example to understand the concept better.