A rhombus is a parallelogram having four congruent sides, that is, of the same length. It does not need to have right angles. There are three formulas for calculating the area of a rhombus. Follow the instructions provided in this article to find out how to calculate the area of any rhombus.
Steps
Method 1 of 3: Using Diagonals
Step 1. Find the length of each diagonal of the diamond
The diagonals are represented by the two straight lines that join the opposite vertices of the parallelogram and meet in the center of the figure. The diagonals of a rhombus are perpendicular to each other and give rise to four sections of the figure that represent right-angled triangles.
Assume that the diagonals of the rhombus are 6 and 8 cm long
Step 2. Multiply the length of the two diagonals together
Continuing with the previous example, you will get the following: 6cm x 8cm = 48cm2. Don't forget to use square units, as you are referencing an area.
Step 3. Divide the result by 2
Given that 6cm x 8cm = 48cm2, dividing the product by 2 you will get 48 cm2/ 2 = 24 cm2. At this point, you can say that the area of the rhombus is equal to 24 cm2.
Method 2 of 3: Use Base Measurement and Height
Step 1. Identify the length of the base and the height of the rhombus
In this case, imagine that the rhombus is resting on one of the sides, so to calculate its area you will need to multiply its height by the length of the base, that is, of one of the sides. Assume that the height of the rhombus is equal to 7 cm and that the base is 10 cm long.
Step 2. Multiply the base by the height
Knowing the length of the rhombus base and its height, all you have to do is multiply the two values together. Continuing with the previous example, you will get 10 cm x 7 cm = 70 cm2. The area of the rhombus under examination is equal to 70 cm2.
Method 3 of 3: Using Trigonometry
Step 1. Calculate the square of any of the sides
A rhombus is characterized by four congruent sides, that is, having the same length, so it does not matter which side you choose to use. Assume that the sides of the rhombus are 2 cm long. In this case, you will get 2cm x 2cm = 4cm2.
Step 2. Multiply the result obtained in the previous step by the sine of one of the angles
Again you can choose any of the four corners of the figure. Assume that one of the angles measures 33 °. At this point, the area of the rhombus will be equal to: (2 cm)2 x sin (33) = 4 cm2 x 0, 55 = 2, 2 cm2. At this point, you can say that the area of the rhombus is equal to 2, 2 cm2.
