Area of a kite

To find the area of a kite, we will use the kite below with a line of symmetry d1. Notice that when d1 is a line of symmetry, the kite is made of 2 triangles.
KiteKite


Area of kite  =  area of triangle ABC + area of triangle ADC

Be careful!

The height of triangle ABC is half d2 or
d2 / 2


Area of triangle ABC =
base × height / 2


base = d1

height =
d2 / 2


The height of triangle ADC is half d2 or
d2 / 2


Area of triangle ADC =
base × height / 2


base = d1

height =
d2 / 2

Area of a kite
Area of a kite
Area of a kite
Area of a kite
Area of a kite
Area of a kite


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.

Formula for the area of a kite

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 d2

d2 = 4 + 4 = 8 meters

The segments with lengths 6 meters and 5 meters must represent d1 then

d1 = 6 meters + 5 meters = 11

Area = (8 × 11) / 2 = 88 / 2 = 44 square meters

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