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 d_{1}d_{2}
AC perpendicular BD
d_{1} = 2 + 8 = 10
d_{2} = 8 + 8 = 16
= 1/2 (10)(16)
= 80
So, area of a kite is 80 in^{2}.
Problem 2 :
Solution :
Area of a kite = 1/2 d_{1}d_{2}
AC perpendicular BD
d_{1} = 3 + 3 = 6
d_{2} = 2 + 4 = 6
= 1/2 (6)(6)
= 18
So, area of a kite is 18 m^{2}.
Problem 3 :
Solution :
Area of a kite = 1/2 d_{1}d_{2}
AC perpendicular BD
d_{1} = 4 + 4 = 8
d_{2} = 6
= 1/2 (8)(6)
= 24
So, area of a kite is 24 ft^{2}.
Problem 4 :
The area of a kite is 120 cm^{2}. 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 cm^{2}
Length of one diagonal d_{1} = 20 cm.
Let length of the other diagonal d_{2} be x.
Area of a kite = 1/2 d_{1}d_{2}
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
x^{2} = AO^{2} + OB^{2} x^{2} = 1^{2} + 2^{2} x^{2} = 1 + 4 x^{2} = 5 x = √5 AB = BC = √5 |
y^{2} = AO^{2} + OD^{2} y^{2} = 1^{2} + 3^{2} y^{2} = 1 + 9 y^{2} = 10 y = √10 AD = 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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