Formula sheet
Area of kite
(1/2) × product of two diagonals is given on the exam formula sheet. You must still know that the two lengths are the diagonals (not the sides), and that in a kite the diagonals cross at right angles.
What the symbols mean
- d₁, d₂ The two diagonals of the kite, the full straight distances across it (length unit).
Given in the exam, or memorise?
(1/2) × product of two diagonals is given on the exam formula sheet. You must still know that the two lengths are the diagonals (not the sides), and that in a kite the diagonals cross at right angles.
Why it works
The diagonals of a kite cut it into right-angled triangles.
- The diagonals of a kite meet at 90°.
- They box the kite inside a rectangle of sides d₁ and d₂.
- The kite fills exactly half of that rectangle, so area = ½ × (d₁ × d₂).
Worked example 1
A kite has diagonals 10 cm and 16 cm. Find its area.
- Area = ½ × (d₁ × d₂)
- = ½ × (10 × 16)
- = ½ × 160
- = 80
Worked example 2
A kite has area 84 cm² and one diagonal 12 cm. Find the other diagonal.
- Area = ½ × (d₁ × d₂)
- 84 = ½ × (12 × d₂)
- 84 = 6 × d₂
- d₂ = 84 ÷ 6 = 14
Where students go wrong
- Using the side lengths of the kite instead of the diagonals.
- Forgetting the ½, which doubles the area.
- Using only half a diagonal, d₁ and d₂ are the full crossing lengths.
- Writing the answer in cm instead of cm².
Use it with
Source:SPM: Format Pentaksiran mulai 2021, Matematik (1449)
Frequently asked questions
Why does the kite area use diagonals, not sides?
Because the diagonals of a kite cross at right angles and split it into four right-angled triangles. That perpendicular crossing lets the two diagonals act like the sides of a surrounding rectangle, and the kite fills half of it.
The slanted sides do not meet at right angles, so they cannot be used the same way.
Does this formula also work for a rhombus?
Yes. A rhombus is a special kite whose diagonals also cross at right angles, so ½ × (d₁ × d₂) gives its area too.
In fact any quadrilateral with perpendicular diagonals follows this rule. Just make sure you are using the full diagonal lengths, not half-diagonals or the side lengths.
How do I find a diagonal when the area is given?
Put the numbers you know into ½ × (d₁ × d₂) = area, then solve for the missing diagonal. For example if area is 84 cm² and one diagonal is 12 cm, then ½ × 12 × d₂ = 84, so 6d₂ = 84 and d₂ = 14 cm.
It is the same formula, just rearranged to make the unknown the subject.