ShapesProperties
- Two pairs of neighbouring sides are equal.
- The diagonals cross at right angles.
- One diagonal is a line of symmetry and cuts the other in half.
- One pair of opposite angles is equal.
- The perimeter is twice the sum of the two different side lengths.
Why the formulas work
The long diagonal splits the kite into two equal triangles. Each has the long diagonal as base and half of the short diagonal as height. Adding the two gives half of p times q. The same formula works for any four-sided shape whose diagonals cross at right angles, which is why the rhombus shares it.
Worked example
Take a kite with diagonal p 10 cm and diagonal q 24 cm.
- Area. Area = ½ × p × q. Here: ½ × 10 × 24 = 120 cm².
Finding a missing measurement
If the area and one diagonal are known, the other diagonal is 2 × area ÷ the known one: an area of 120 cm² and a diagonal of 10 cm give 24 cm for the other. The sides come from Pythagoras, because the diagonals cross at right angles. Take a kite whose diagonals are 24 cm and 21 cm, with the longer one cut into 5 cm and 16 cm. Its sides are √(144 + 25) = 13 cm and √(144 + 256) = 20 cm, its perimeter is 2 × (13 + 20) = 66 cm and its area is ½ × 24 × 21 = 252 cm². A kite can also point inwards like an arrowhead, when it is called a dart. The area formula holds for that shape too.
Mistakes to avoid
- Multiplying the two side lengths. The area needs the diagonals.
- Forgetting to halve the product of the diagonals.
Where you see it
Paper kites flown at Makar Sankranti and Basant, some earrings and road-sign backings are kite shaped.
Try these
Work each one out, then tap to check.
A kite has diagonal p 12 cm and diagonal q 30 cm. Find its area.
Area = 180 cm².
A kite has diagonal p 9 cm and diagonal q 16 cm. Find its area.
Area = 72 cm².