Perimeter of a Kite Formula

Kite is a quadrilateral in which two pairs of sides are equal and these equal sides are adjacent to each other. It is known as a parallelogram, it also has two pairs of equal sides but in a parallelogram, those pairs are opposite to one another while in the case of kite these equal pairs of sides are adjacent.

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In the above figure, two adjacent sides are equal so the length of both is a and the length of the other two equal sides are b.

p and q are the diagonals of the Kite.

Properties of Kite

• Kite has four sides and its geometry is similar to the quadrilateral type.
• It has four angles and four vertices.
• It has a single line of symmetry.
• Diagonals of a kite intersect at right angles.
• The length of diagonals of a kite is not equal.
• Rotational symmetry is of order 1.
• Each angle formed by adjacent unequal sides is equal.
• Each angle formed by adjacent equal sides is unequal.

Perimeter of a Kite Formula

Perimeter is the sum of all sides of a closed polygon. So to calculate the perimeter of a kite, the length of all the sides are required, or we can say only two unequal sides are required, lets call these two unequal sides a and b.

Perimeter of Kite = Sum of all sides = a+a+b+b = 2 × (a + b)

Sample Questions

Question 1: Find the perimeter of a kite whose sides are 4 cm, 4 cm, 6 cm, 6 cm?

Answer: 

Perimeter of Kite = sum of all sides

                            = 4 + 4 + 6 + 6

                            = 20 cm

Question 2:Find the perimeter of a kite whose unequal sides are 8 cm and 12 cm?

Answer:

Given a = 8 cm and b = 12 cm.

Perimeter of Kite = 2 × (a+b)

                            = 2 × (8+12)

                            = 40 cm

Question 3: Perimeter of a kite is 50 cm, and a side length is 4 cm find the length of other unequal side?

Answer: 

Given perimeter = 50 cm, lets take 4 cm as a 

We need to find b.

using formula of perimeter of kite = 2×(a+b)

                                                 50 = 2×(4 + b)

                                                 50 = 8 + 2×b

                                                ×b = 50 - 8

                                                  b = 42/2

                                                  b = 21 cm

Hence the length of other unequal side is 21 cm.

Question 4: If one side of akite is twice the other unequal side and theperimeter is 99 cm, find both the unequal sides?

Answer: 

Let take first unequal side is A,

then according to question A = 2×B

                                        so B = A/2

perimeter of kite = 2×(A+B)

                          102  = 2×(A+A/2)                  as B = A/2

                          102  = 2×((3×A)/2) 

                          102  = 3×A

                           A = 102/3

                           A = 34 cm

                           B = A/2 = 34/2 = 17 cm 

Hence unequal sides are of length 17 cm and 34 cm.

Question 5: Perimeter of a kite is 100 cm, and thelength of one side is 42 cm find the length of another unequal side?

Answer: 

Given perimeter = 100 cm, lets take 42 cm  as a

we need to find b.

using formula of perimeter of kite = 2×(a+b)

                                                100  = 2×(42 + b)

                                               100  = 84 + 2×b

                                               2×b = 100 - 84

                                                 b = 16/2

                                                 b = 8 cm

Hence the length of other unequal side is 8 cm.