What is a kite?
A closed polygon having four vertices, four sides and four angles is considered to be a quadrilateral. A kite is a quadrilateral in which each pair of the adjacent sides is congruent, but the opposite sides are not congruent. A rhombus can be considered a kite with all its four sides being congruent. Shown in the image is a kite with sides RQ, QP, RS and RS. The kite has two diagonals RP and QS represented by \(D_1\) and \(D_2\).
Properties of a Kite
- Angles between the unequal sides of a kite are equal.
- View the kite as a pair of congruent triangles having a common base.
- The diagonals of a kite intersect such that the angle formed between them is 90 degrees.
- The longer diagonal is the perpendicular bisector of the shorter diagonal.
- A kite is symmetrical about its longer diagonal.
- The shorter diagonal divides the kite into two isosceles triangles.
Formula for the Area of a kite
The area of the kite is half the product of its diagonals, that is A = \(\frac{1}{2}\) x \(d_1\) x \(d_2\)
In this formula, \(d_1\) and \(d_2\) are the lengths of the diagonals of the kite.
Solved Examples
Example 1: The longer and shorter diagonals of a kite are 24 cm and 14 cm in a kite. What is the area of a kite?
Solution: As stated in the question,
Length of longer diagonal, \(d_1\) = 24 cm
Length of shorter diagonal, \(d_2\) = 14 cm
Area of a Kite, A = \(\frac{1}{2}\) x \(d_1\) x \(d_2\)
A = \(\frac{1}{2}\) x 24 x 14
= 24 x 7
= 168 cm\(^2\)
So, the area of a kite is 168 square centimeters.
Example 2: The area of a kite is 420 square centimeters and one of its diagonals is 24 centimeter long. Find the length of the other diagonal.
Solution: The details given are,
Area of a kite, A = 420 cm²
Length of one diagonal, d\(_1\) = 24 cm
Area of a Kite formula,
A = \(\frac{1}{2}\) x \(d_1\) x \(d_2\)
420 = \(\frac{1}{2}\) x 24 x \(d_2\)
\(d_2\) = \(\frac{840}{24}\)
\(d_2\) = 35 cm
So, the other diagonal of the kite is 35 centimeters long.
Example 3: Sam, Cathay, Simon and Betty are four friends flying kites of the same size in a park. 13 inch and 16 inch are the lengths of the diagonals running across each kite. Determine the sum of areas of all the four kites.
Solution:
Lengths of diagonals are:
\(d_1\) = 13 in
\(d_2\) = 16 in
The area of each kite is:
A = \(\frac{1}{2}\) x \(d_1\) x \(d_2\)
= \(\frac{1}{2}\) x 13 x 16
= 104 in\(^2\)
Since each kite is of the same size, therefore the total area of all the four kites is 4 × 104 = 416 in\(^2\)
Therefore, the area of the four kites is 416 square inches.
A kite is a quadrilateral in which the four sides can be grouped into two pairs of sides that are equal and adjacent to each other. However, only one pair of opposite angles are equal. In contrast, all the sides of a rhombus are equal, and the opposite angles are equal.
When finding the area of a kite, we calculate the space covered by it on a two dimensional plane.
Only one pair of opposite angles that appear between the non-congruent sides are equal to each other.
No, a parallelogram has opposite sides that are equal and parallel to each other. Such characteristics are not seen in a kite.