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Last modified on August 3rd, 2023

The area of a kite is the total space enclosed by it. The area is expressed in square units such as cm^{2}, in^{2}, m^{2}, ft^{2}, yd^{2}, etc. This article will precisely help you find the area of a kite.

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

**Area (A) = (d _{1} × d_{2})/2, here d_{1} and d_{2} are the diagonals**

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

In kite ABCD, diagonals AC = d_{1}, and BD = d_{2}

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 = d_{1}, OB = d_{2}/2

= 1/2 × d_{1} × d_{2}/2

= 1/4 × d_{1} × d_{2}

In ΔADC, base = AC, height = OD

∴ Area of ΔADC = 1/2 × AC × OD, here AC = d_{1}, OD = d_{2}/2

= 1/2 × d_{1} × d_{2}/2

= 1/4 × d_{1} × d_{2}

As we know,

Area of kite ABCD = Area of ΔABC + ΔADC

= (1/4 × d_{1} × d_{2}) + (1/4 × d_{1 }× d_{2})

= (d_{1} × d_{2})/2

So the above derivation is the proof of area of a kite as 1/2 × d_{1} × d_{2}

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) = (d_{1} × d_{2})/2**, here d

∴A = (30 × 24)/2

= 360 cm

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 cm^{2}

Last modified on August 3rd, 2023