# FINDING AREA OF KITE

Area of kite ?

A kite is a quadrilateral which has two pairs of adjacent sides equal in length.

To find area of kite we need diagonals.

Area of kite = (1/2) x diagonal 1 x diagonal 2

Find the area of each kite.

Problem 1 :

Solution :

Area of a kite = 1/2 d1d2

AC perpendicular BD

d1 = 2 + 8 = 10

d2 = 8 + 8 = 16

= 1/2 (10)(16)

= 80

So, area of a kite is 80 in2.

Problem 2 :

Solution :

Area of a kite = 1/2 d1d2

AC perpendicular BD

d1 = 3 + 3 = 6

d2 = 2 + 4 = 6

= 1/2 (6)(6)

= 18

So, area of a kite is 18 m2.

Problem 3 :

Solution :

Area of a kite = 1/2 d1d2

AC perpendicular BD

d1 = 4 + 4 = 8

d2 = 6

= 1/2 (8)(6)

= 24

So, area of a kite is 24 ft2.

Problem 4 :

The area of a kite is 120 cm2. The length of one diagonal is 20 cm. what is the length of the other diagonal?

a) 12cm     b) 20 cm       c) 24 cm     d) 48 cm

Solution :

Given, area of a kite is 120 cm2

Length of one diagonal d1 = 20 cm.

Let length of the other diagonal d2 be x.

Area of a kite = 1/2 d1d2

120 = 1/2 (20)(x)

120 = 10x

Divide both sides by 10.

120/10 = 10x/10

12 = x

So, length of the other diagonal is12 cm.

Problem 5 :

A kite has vertices at the points (2, 0) (3, 2) (4, 0) and (3, -3). Find the perimeter and area of the kite.

Solution :

Let the given points be A (2, 0) B (3, 2) C (4, 0) and D (3, -3)

Finding area :

Area of kite = (1/2) x AC x BD

AC = 2 units

BD = 5 units

= (1/2) x 4 x 5

= 10 square units.

Finding perimeter :

To find the perimeter of the kite, we need length of all sides. To figure out the length of the sides, we may use Pythagorean theorem.

Finding Perimeter :

Let AB = x

We know that diagonals of a kite bisect each other at right angles. Let O be the point of intersection of diagonals.

Using Pythagorean theorem, we get

 x2 = AO2 + OB2 x2 = 12 + 22 x2 = 1 + 4x2 = 5x = √5AB = BC = √5 y2 = AO2 + OD2 y2 = 12 + 32 y2 = 1 + 9y2 = 10y = √10AD = DC = √10

Perimeter of kite ABCD = 2√5 + 2√10

= 2(2.23) + 2(3.16)

= 10.78 units.

So, perimeter of the kite is 10.78 units.

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