Introduction to Area of a Kite Formula
A quadrilateral is a polygon that can be defined as a closed, two-dimensional shape which has four straight sides. There are different types of quadrilateral. In this article, we will discuss one of its type i.e Kite also kite area and perimeter formula. We will discuss the properties of the kite and proof for the area of a kite. In Euclidean geometry, a kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.
Definition of Kite:
Kite is a special type of quadrilateral in which each pair of the consecutive sides is congruent, but the opposite sides are not congruent. Rhombus is a kite with all the four sides congruent.
The diagonals of a kite are perpendicular. Area of a kite is given as half of the product of the diagonals which is similar to that of a rhombus. The formula for kite area is given below:
Area formula of kite = 1/2 × d1 × d2
Where d1 = Longer diagonal of kite.
d2 = Shorter diagonal of kite.
Perimeter of Kite Formula
A kite has two pairs of equal size. Perimeter is defined as the total distance around the outside of a kite. Total distance can be found by calculating the sum of the lengths of each pair.
The perimeter formula of a kite is,
Perimeter = 2a + 2b
Where a is the length of the first pair and b is the length of the second pair.
Properties of a Kite:
Angles between unequal sides are equal.
A kite has a pair of congruent triangles with a common base.
Kite has two diagonals and both intersect each other at right angles.
The longer diagonal is the perpendicular bisector of the shorter diagonal.
A kite is symmetrical about its main diagonal.
The shorter diagonal divides a kite into two isosceles triangles.
Proof for Area of a Kite
Let us consider a kite ABCD. Let diagonals AB(D1) and CD(D2) meet at point E. From the diagram, we see that a diagonal divides a kite into two triangles.
In the figure given above, we see that diagonal AB divides a kite in two triangles ACB and ADB.
Thus formula to find area of kite is equal to:
Area(△ACB) = 1/2 × AB × CE
and, Area(△ADB)= 1/2 × AB × DE
Area of a kite (ABCD) is equal to the sum of the area of both the triangles.
Area of a Kite =Area(△ACB) + Area(△ADB)
= 1/2 AB × CE + 1/2 AB × DE
AB is common in both the triangle take it out
Area of a Kite = 1/2 AB × (CE + DE)
From the above figure, we can write CD = (CE + DE)
Hence, Area of a Kite = 1/2 AB × CD = 1/2 × D1 × D2
Now replace AB by D1 and CD by D2
Therefore, formula to find the area of a kite = 1/2 × D1 × D2 is proved.
Solved Examples
1. Find the perimeter of the kite whose equal sides are 15 cm and 24 cm.
Solution: Given the length of equal sides,
Let a, b be the length of equal side
a = 15 cm and b = 24 cm
The formula of the perimeter of the kite = 2(a + b)
Perimeter of the kite = 2(15 + 24) = 2 × 39
Perimeter of the kite = 78 cm
Hence, the perimeter of the kite is 78 cm.
2. Area of a kite is 120 cm2 and one of its diagonals is 20 cm long. Find the length of the other diagonal.
Solution: Given,
Area of a kite = 120 cm2
Length of one diagonal = 20 cm
Area of Kite = 1/2 × d1 × d2
120 = 1/2 × 12 × d2
d2 = 12cm
Therefore, the length of the other diagonal = 12 cm.
FAQs on Area of a Kite Formula
1. Is Every Kite a Rhombus?
Ans: A kite is a quadrilateral having four sides that can be grouped into two pairs of equal-length sides that are adjacent to each other and only one pair of opposite angles are equal. Hence we can say that all sides of a rhombus are equal and opposite angles are equal. So, every kite is not a rhombus.
2. Is a Kite Symmetrical?
Ans: Yes, kites are symmetrical. It has one line of symmetry and also rotational symmetry of order one.
3. Why is a Rectangle not a Kite?
Ans: A kite cannot be the same as a rectangle because at any time two pairs of adjacent sides are equal in a kite, but not so in a rectangle. Also, two diagonals intersect at right angles in a kite, but not so in a rectangle.
