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A shape’s perimeter is defined as the total distance around the shape. Essentially, it is the length of any shape when expanded in a linear form. Depending on their dimensions, the perimeters of different shapes can match in length.
For example, if a circle is made of a metal wire of length L, the same wire can be used to make a square with equal-length sides.
A kite has two equal-sized pairs. The total distance around the outside is referred to as the kite’s perimeter. This distance can be calculated by adding the lengths of each pair.
Types of Kite
There are two type of Kites:
1. Concave Kite
2. Convex Kite
What are the Properties of Kite?
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Two distinct pairs of adjacent sides are congruent
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Kite diagonals intersect at right angles
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One of the kite diagonals is the perpendicular bisector of another.
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Angles between unequal sides are equal.
Symmetry of Kite
The quadrilaterals with an axis of symmetry along one of their diagonals are called kites. Any non-self-crossing quadrilateral with an axis of symmetry must be either a kite (if the axis of symmetry is a diagonal) or an isosceles trapezoid (if the axis of symmetry passes through the midpoints of two sides); special cases include the rhombus and rectangle, which each have two axes of symmetry, and the square, which is both a kite and an isosceles trapez. If crossings are permitted, the list of quadrilaterals with symmetric axes must be expanded to include antiparallelograms.
The Sides and Angles of a Kite |
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There are two sets of adjacent sides that are the same length (next to each other) (congruent.) There is only one set of angles that are congruent. These are opposite each other as well as are located between sides of varying lengths. It’s difficult to put this stuff into words that aren’t confusing. So, take a look at the image! |
Area and Perimeter of Kite
The perimeter of kite formula is given below,
Perimeter of kite formula = 2a+2b
Where,
a equals the length of the first pair
b equals the length of the second pair
The region bounded by an object’s shape is referred to as its area. The area of a shape is the space covered by the figure or any geometric shapes. The area of all shapes is determined by their dimensions and properties. Different shapes have various areas. The area of the square is not the same as the area of the kite.
If two objects have a similar shape, the area covered by them does not have to be equal unless and until the dimensions of both shapes are also equal.
Area of kite equals pq/2
Where, p and q are diagonals of a kite
Solved Example
Question 1: Find the perimeter of the kite whose equal sides are 18 cm and 26 cm.
Solution:
Given,
a = 18 cm
b = 26 cm
Perimeter of kite formula = 2(a + b)
Perimeter of kite = 2(18 + 26) = 2 × 44
Perimeter of kite = 88 cm
Question 2: Find the perimeter of the kite whose equal sides are 5 cm and 10 cm.
Solution:
Given,
a = 5 cm
b = 10 cm
Perimeter of kite formula = 2(5 + 10)
Perimeter of kite = 2(5 + 10) = 2 × 15
Perimeter of kite = 30 cm