Area of a Kite: Overview, Questions, Preparation

Did you know that the kite you enjoy flying is of a geometrical shape? Like the parallelogram and rhombus, it is also a special quadrilateral with its own unique properties. First, let’s have a look at them.

Properties of a Kite

• It has a pair of equal adjacent sides.
• Opposite angles between unequal sides are equal.
• A kite has two pairs of congruent triangles with a common base.
• Diagonals of a kite intersect each other at right angles(90°).
• The diagonals bisect each other perpendicularly.

The formula of the area of the kite:

Area of Kite= (D1 x D2)/2 

Where D1 and D2 are the two diagonals of the kite.

Let us have a quick look at how this formula is derived. 

Consider the area of the following kite PQRS.

Here the diagonals are PR and QS
Let diagonal PR =a and diagonal QS = b
Diagonals of a kite cut one another at right angles as shown by the diagonal PR bisecting the diagonal QS.

OQ = OS = QS/2= b/2 

Area of the kite = Area of triangle PQR + Area of triangle PSR
Area of Triangle = ½ ×base×height
Here, base = a and height = OQ = OS= b/2
Area of triangle PQR = ½ × a × b/2 
Area of triangle PSR=  ½ × a/2 × b 
Area of Kite PQRS= (½ × a × b/2) + (½ × a/2 × b)
                                = ½ × ab 

Students are made familiar with the concept of mensuration in class 6. They will continue learning this topic until their class 10th. As they move each class ahead, they will encounter multiple complex numerical with the primary application of mensuration till class 12. But this is one of those topics for which students will witness more practical application in their daily lives than any other.

1.Find the area of a kite with diagonals that are 6 inches and 18 inches long.
 Solution:

Area of a kite = d1*d2/ 2
= (6 x 18) /2
= 108/2
= 54 square inches.

2. When the diagonals of a kite meet, they make four segments with lengths of 6 meters, 4 meters, 5 meters, and 4 meters. What is the area of the kite?
Solution:

The segments with lengths 4 meters and 4 meters must represent the segment that was bisected pieces or d,
Therefore
d, = 4 +4 = 8 meters
The segments with lengths 6 meters and 5 meters must represent d, then
d, = 6 meters + 5 meters = 11
Area of a kite = ½ (d, x d,)
                        = (8 x 11)/2
                          =88/2 = 44 meter sq.

3. Find the kite area whose long and short diagonals are 22 cm and 12cm respectively.
Solution:

Given,
Length of longer diagonal, D1= 22 cm
Length of shorter diagonal, D2= 12 cm
Area of Kite =  ½ * D1 * D2
Area of kite = ½  x 22 x 12 = 132 cm sq

4. Area of a kite is 126 cm², and one of its diagonals is 21cm long. Find the length of the other diagonal.
Solution:

Given,
Area of a kite =126 cm²
Length of one diagonal = 21 cm
Area of the kite= (d1*d2)/ 2
             126       =  21*d2/2
             d2= 126*2/21
                 = 12cm

Q: What is a kite?

Q: What is the perimeter of the kite?

Q: What is the area of a kite?

Q: Are the diagonals of the kite equal?

Q: Is a kite a symmetrical figure?