Area of a rhombus
There are several formulas that can be used to find the area of a rhombus depending on the known parameters.
The area, A, of a rhombus is half the product of its two diagonals.
where d1 and d2 are the lengths of the two diagonals.
Referencing rhombus ABCD above, Let AC = d1 and BD = d2. The diagonals of a rhombus are perpendicular to each other, so AC⟂ DB. Rhombus ABCD can be decomposed into triangles ABC and ADC. The area of △ABC = where BE is the altitude of △ABC. The area of △ADC = where DE is the altitude of △ADC. The area of rhombus ABCD equals the sum of the areas of △ABC and △ADC.
|△ABC + △ADC =|
If the area of a rhombus is 230, and one of its diagonals is 10, what is the length of the other diagonal?
Let d1 = 10. Since A = 230 we can find d2 as follows:
230 = 5 × d2
d2 = 46
Using side and height
Since a rhombus is also a parallelogram, we can use the formula for the area of a parallelogram:
A = b×h
where b is the base or the side length of the rhombus, and h is the corresponding height.
Using side and angle
If the side length and one of the angles of the rhombus are given, the area is:
A = a2 × sin(θ)
where a is side length and θ is one of the angles.
Finding area using a grid
Another way to find the area of a rhombus is to determine how many unit squares it takes to cover its surface. Below is a unit square whose dimensions are 1 cm.
A grid of unit squares can be used when determining the area of a rhombus.
The grid above contains unit squares that have an area of 1 cm2 each. The rhombus on the left contains 8 full squares and 12 partial squares, so it has an area of approximately:
The rhombus to the right contains 25 full squares, so it has an area of approximately 25 cm2.
This method can be used to find the area of any shape; it is not limited to rhombuses. However, it is only an approximate value of the area. The smaller the unit square used, the higher the accuracy of the approximation. Using a grid made up of 1 mm squares is 10 times more accurate than using a grid made up of 1 cm squares.