Kite

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What is a Kite?

A quadrilateral is defined as a closed polygon with four vertices, four sides, and four angles. Two pairs of adjacent sides of a kite are congruent, but the opposite sides are not. Rhombuses can be compared to kites because they have four congruent sides. A kite EKIT with the sides EK, KI, IT, and TE is shown below. The diagonals of a kite are KT and EI are denoted by the letters d1${�}_1$ and d2${�}_2$, respectively.

 

Properties of a Kite

A kite has the following properties:

• Angles formed between the uneven sides of a kite are equal in measure
• Consider the kite as two congruent triangles with a single base (longer diagonal)
• The diagonals of a kite intersect each other at right angles

• The shorter diagonal is bisected perpendicularly by the longer diagonal

• A kite is symmetrical about its longer diagonal
• The kite is split into two isosceles triangles by the shorter diagonal

Perimeter of a Kite

The perimeter of a kite is calculated by adding the side lengths of each pair of sides. Let’s look at the formula to find the perimeter of a kite.

 

Perimeter of a Kite (P) = 2(a + b)

 

Where a and b are the side lengths of the kite.

 

Formula for the Area of a Kite

The area of the kite is half the product of its diagonals, that is, A = 12×d1×d2$\frac{1}{2}\times {�}_1\times {�}_2$.

 

In this formula, d1${�}_1$ and d2${�}_2$ are the lengths of the diagonals of the kite.

 

Solved Examples

Example 1: The length of the diagonals of a kite are 12 cm and 6 cm. Find the area of a kite?

 

Solution:

Length of longer diagonal, d1${�}_1$ = 12 cm

 

Length of shorter diagonal, d2${�}_2$ = 6 cm

 

Area of Kite, A = 12×d1×d2$\frac{1}{2}\times {�}_1\times {�}_2$

 

A = 12×12×6$\frac{1}{2}\times 12\times 6$   [Write the formula]

 

= 12 x 3               [Divide 6 by 2]

 

= 36 cm2${}^2$             [Multiply]

 

So, the area of the kite is 36 square centimeters.

 

Example 2: The area of a kite is 144 square centimeters and one of its diagonals is 24 centimeters long. Find the length of the other diagonal.

 

Solution:

The question states that,

 

Area of a kite, A = 144 cm²

 

Length of one diagonal, d1${�}_1$ = 24 cm

 

Area of Kite formula

 

A = 12×d1×d2$\frac{1}{2}\times {�}_1\times {�}_2$      [Write the formula]

 

144 = 12×24×d2$\frac{1}{2}\times 24\times {�}_2$   [Substitute the value]

 

288 = 24 x d2${�}_2$          [Multiply each side by 2]

 

d2${�}_2$ = 28824$\frac{288}{24}$                   [Divide each side by 24]

 

d2${�}_2$ = 12 cm               [Simplify]

 

So, the other diagonal of the kite is 12 centimeters.

 

Example 3: Robert, James, Chris and Mark are four friends flying kites of the same size in a park. 15 inch and 20 inch are the lengths of the diagonals running across each kite. Determine the sum of areas of all the four kites.

Solution:
Lengths of the diagonals are:

d1${�}_1$ = 15 in

 

d2${�}_2$ = 20 in

The area of each kite is:

A = 12×d1×d2$\frac{1}{2}\times {�}_1\times {�}_2$

= 12×15×20$\frac{1}{2}\times 15\times 20$

= 150 in2${}^2$

Since each kite is of the same size, therefore the total area of all the four kites is 4 × 150 = 600  in2${}^2$.

Therefore, the area of the four kites is 600 square inches