To find the area of a rhombus, there are three common formulas depending on the information you have:
- Using base and height:
Area=base×height\text{Area}=\text{base}\times \text{height}Area=base×height
This is similar to the area formula for parallelograms since a rhombus is a special type of parallelogram
- Using the lengths of the diagonals:
Area=12×d1×d2\text{Area}=\frac{1}{2}\times d_1\times d_2Area=21×d1×d2
where d1d_1d1 and d2d_2d2 are the lengths of the diagonals of the rhombus. The diagonals are perpendicular and bisect each other, making this formula very useful
- Using the side length and an interior angle:
Area=s2×sin(θ)\text{Area}=s^2\times \sin(\theta)Area=s2×sin(θ)
where sss is the length of a side and θ\theta θ is any interior angle of the rhombus. This formula uses trigonometry and works because the sine of an angle and its supplementary angle are equal
Summary of formulas:
Given| Formula
---|---
Base and height| Area = base × height
Diagonals d1d_1d1 and d2d_2d2| Area = 12×d1×d2\frac{1}{2}\times d_1\times
d_221×d1×d2
Side length sss and angle θ\theta θ| Area = s2×sin(θ)s^2\times
\sin(\theta)s2×sin(θ)
These formulas cover most cases for calculating the area of a rhombus depending on what measurements are available
