Area of a kite
To find the area of a kite, we will use the kite below with a line of symmetry d
_{1}. Notice that when d
_{1} is a line of symmetry, the kite is made of 2 triangles.
Kite
Area of kite = area of triangle ABC + area of triangle ADC
Be careful!
The height of triangle ABC is half d
_{2} or
d_{2}
/
2
Area of triangle ABC =
base × height
/
2
base = d
_{1}
The height of triangle ADC is half d
_{2} or
d_{2}
/
2
Area of triangle ADC =
base × height
/
2
base = d
_{1}
Here is the formula for the area of a kite.
Once you know the length of the diagonals, you can just multiply them and divide the result by 2.
Examples
1 ) Find the area of a kite with diagonals that are 6 inches and 18 inches long.
Area = (6 × 18) / 2 = 108 / 2 = 54 square inches.
2)
When the diagonals of a kite meet, they make 4 segments with lengths 6 meters, 4 meters, 5 meters, and 4 meters. What is the area of the resulting kite.
The segments with lengths 4 meters and 4 meters must represent the segment that was bisected into 2 equal pieces or d
_{2}
d
_{2} = 4 + 4 = 8 meters
The segments with lengths 6 meters and 5 meters must represent d
_{1} then
d
_{1} = 6 meters + 5 meters = 11
Area = (8 × 11) / 2 = 88 / 2 = 44 square meters

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