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.

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

Be careful!

base = d₁







base = d₁

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 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