Question

find the area and preimeter of a kite​

Answer 1

Answer:

Formula for Area of a Quadrilateral

The diagonals of a kite are perpendicular. Area of a kite is given as half of the product of the diagonals which is same as that of a rhombus. Area of a kite can be expressed by the formula:

Area of Kite = 12D1D2

D1 = long diagonal of kite

D2 = short diagonal of kite

Derivation for Area of a Kite:

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 diagonal PR bisecting diagonal QS.

OQ = OS = OS2=b2

Area of the kite = Area of triangle PQR + Area of triangle PSR

Area of Triangle = 12base×height

Here, base = a and height = OQ = OS= b/2

Area of triangle PQR = 12×a×b2

Area of triangle PSR= 12×a×b2

Area of the kite = 12×a×b2 + 12×a×b2

= ab4+ab4

= 2ab4=12ab

Hence,

Area of the kite = 12PR∗QS= Half of the product of the diagonals

Note:

If lengths of unequal sides are given, using Pythagoras theorem, the length of diagonals can be found. The area of a kite can be calculated by using the lengths of its diagonals.

Solved Examples:

Example 1: Find the area of kite 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 =12D1D2

Area of kite = 12 x 22 x 12 = 132cm2

Example 2: Area of a kite is 126 cm² and one of its diagonal 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 Kite =12D1D2

126=12×21×D2

D2 = 12cm

Step-by-step explanation:

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Answer 2

Answer:

Formula for area of kite

The diagonals of a kite are perpendicular. Area of a kite is given as half of the product of the diagonals which is same as that of a rhombus. Area of a kite can be expressed by the formula:

Area of Kite = 12D1D2

D1 = long diagonal of kite

D2 = short diagonal of kite

Formula for perimeter of kite

A kite has two pairs of equal size. Total distance around the outside is called the perimeter of a kite. This 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 = The length of the first pair

b = The length of the second pair

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