Area of a rhombus or kite
Rhombi and kites have a simple area pattern: use the diagonals. If the problem gives the full lengths of the diagonals, the area is
[A=\frac{d_1 d_2}{2}]
where (d_1) and (d_2) are the diagonals.
Method
- Read the diagonal lengths carefully. Make sure you are using the full diagonal, not half of it.
- Multiply the diagonals.
- Divide by 2. This gives the area.
- Simplify the final answer. Keep exact values if the exercise uses them.
Important idea
This formula works because the diagonals split a rhombus or kite into four triangles with equal combined area. It is often easier than trying to use base and height.
Check your work
- The answer should be in square units.
- If the diagonals are measured in the same unit, the area should match that unit squared.
- A quick reasonableness check: the area should be smaller than the rectangle with side lengths equal to the diagonals.
Example structure
If the diagonals are 10 and 6, then
[A=\frac{10\cdot 6}{2}=30]
so the area is 30 square units.