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 \(d_1\) and \(d_2\), 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 = \(\frac{1}{2}\times d_1 \times d_2\).
In this formula, \(d_1\) and \(d_2\) 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, \(d_1\) = 12 cm
Length of shorter diagonal, \(d_2\) = 6 cm
Area of Kite, A = \(\frac{1}{2}\times d_1 \times d_2\)
A = \(\frac{1}{2}\times 12 \times 6\) [Write the formula]
= 12 x 3 [Divide 6 by 2]
= 36 cm\(^2\) [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, \(d_1\) = 24 cm
Area of Kite formula
A = \(\frac{1}{2}\times d_1 \times d_2\) [Write the formula]
144 = \(\frac{1}{2}\times 24 \times d_2\) [Substitute the value]
288 = 24 x \(d_2\) [Multiply each side by 2]
\(d_2\) = \(\frac{288}{24}\) [Divide each side by 24]
\(d_2\) = 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:
\(d_1\) = 15 in
\(d_2\) = 20 in
The area of each kite is:
A = \(\frac{1}{2}\times d_1 \times d_2\)
= \(\frac{1}{2}\times 15 \times 20\)
= 150 in\(^2\)
Since each kite is of the same size, therefore the total area of all the four kites is 4 × 150 = 600 in\(^2\).
Therefore, the area of the four kites is 600 square inches.
No, only a pair of angles formed between the non congruent sides are equal.
A parallelogram has opposite sides that are congruent and parallel to one another but this is not so in a kite. So, kites are not considered to be parallelograms.
In case all the sides of a kite are equal, we are then looking at a rhombus and this shape with equal sides follows all the properties of a rhombus.
The area of a kite is half the product of its diagonals.