Calculate the area of the rhombus is very easy with our free online calculator. The only data we need to know are the values that measure the major diagonal and minor diagonal of the polygon. If you have them, enter the numbers in the tool, press the calculate button and you will get the area of the rhombus immediately.
Remember that it is imperative that the units of origin matchthat is, both in centimeters, meters or whatever. You can always use our length unit converter if you have to make any transformations to meet this requirement.
How to calculate the area of a rhombus
To get the area of a rhombus you have to apply the following mathematical formula:
You simply have to know that:
- D is the length of the longest diagonal
- d is the length of the minor diagonal
With this data we can now remove the surface of the rhombus. If you want to find the area of a rhomboidPlease click on the link we have just left you, as they are different figures.
Finally, the unit of the rhombus area will be squared. For example, if the smaller diagonal measures 2 centimeters and the larger diagonal measures 3 centimeters, the area of the polygon will be 3 square centimeters.
As a solved exercise, let's calculate the area of a rhombus whose major diagonal D = 6 cm and the minor diagonal is d = 3 cm. To solve it, we apply the formula that you have above these lines and we have that:
Area of rhombus = (6cm x 3cm) / 2 = 18 / 2 = 9 cm2
How to calculate the diagonals of a rhombus
If we are asked to calculate the diagonals of a rhombuswe have to use this formula:
4a2 = D2 + d2
- a: the length of one of the sides of the rhombus
- D: the length of the longest diagonal
- d: the length of the minor diagonal
Depending on the diagonal of the rhombus we want to calculate, we will have to isolate one unknown or another. Below you have the formula to be used for each of the diagonals that has the rhombus..:
d = √(4a2 - D2)
D = √(4a2 - d2)
Remember that in both cases, the square root has to be applied to everything inside the parenthesis.
Calculate the area of a rhombus from the perimeter.
The rhombus is a figure that has four equal sides, therefore, its perimeter is:
perimeter = 4a
From the perimeter and the length of one of the diagonals we can derive the area combining all the theory we have seen so far.
For example, let's calculate the area of a rhombus whose minor diagonal is d = 4 cm and y has a perimeter of 32 cm.
The first thing we will do with the data of the statement is to find how long each side of the rhombus is. To do this we clear the unknown 'a' from the previous formula:
a = perimeter / 4 = 32 cm / 4 = 8 centimeters.
Next we will calculate how long the diagonal is that we are missing, that is, the largest one. To obtain its length we will take the formula we have seen in the previous point:
D = √(4a2 - d2) = √(4 x 82 – 42) = √(256 - 16) = √240 = 15,49
Finally, we have all the data to calculate the area:
Area of rhombus = (15,49cm x 4cm) / 2 = 18 / 2 = 30,98 cm2
If you have any questions about how to calculate the area of a rhombusIf you do not know how to solve an exercise, leave us a comment with the exercise you do not know how to solve and we will help you.