# 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.

Find the area of a kite whose diagonals are 30 cm and 24 cm.

Solution:

As we know,
Area (A) = (d1 × d2)/2, here d1 = 30 cm, d2 = 24 cm
∴A = (30 × 24)/2
= 360 cm2

### 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.

Finding the area of a kite when ADJACENT SIDES and ANGLE are known

What is the area of a kite given?

Solution:

As we know,
Area (A) = a × b × sin(θ), here a = 11.5 cm, b = 27.8 cm, θ = 120°
∴ A = 11.5 × 27.8 × sin(120)
= 319.7 × √3/2
= 276.87 cm2