How to Calculate the Area of a Rhombus

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Last Updated: September 23, 2024 Fact Checked

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A rhombus is a parallelogram with four congruent sides. It does not have to have right angles.^{[1]
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Research source} There are three formulas for finding the area of a rhombus. Just follow these steps if you want to know how to do it.

Method 1

Method 1 of 3:

Using the Diagonals

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Find the length of each diagonal. The diagonals of a rhombus are the lines that connect the opposite vertices (corners) in the center of the shape. The diagonals of a rhombus are perpendicular and form four right triangles through their intersection.^{[2]
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- Let's say the diagonals are 6 cm. and 8 cm. long.
Just write down the length of the diagonals and multiply them. In this case, 6 cm x 8 cm = 48 cm². Don't forget to square the units since you're working in square units.^{[3]
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Since 6 cm x 8 cm = 48 cm², just divide the result by 2. 48 cm²/2 = 24 cm². The area of the rhombus is 24 cm².^{[4]
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Method 2

Method 2 of 3:

Using the Base and Height

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Research source} You can also think of this as multiplying the altitude of the rhombus with the length of the side of the rhombus. Let's say the height of the rhombus is 7 cm and the base is 10 cm.
Once you know the base and height of the rhombus, all you have to do to find the area of the shape is to multiply them. So, 10 cm x 7 cm = 70 cm². The area of the rhombus is 70 cm².^{[6]
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Method 3

Method 3 of 3:

Using Trigonometry

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A rhombus has four equal sides, so it doesn't matter which side you choose. Let's say the side is 2 cm long. 2 cm x 2 cm = 4 cm².^{[7]
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It doesn't matter which angle you choose. Let's say one of the angles is 33 degrees. Just multiply sine (33) by 4 cm² to get the area of the rhombus. (2 cm)² x sine (33) = 4 cm² x 0.55 = 2.2 cm². The area of the rhombus is 2.2 cm².^{[8]
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Rhombus Area Calculator, Practice Problems, and Answers

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How do I find the perimeter of a rhombus?

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Perimeter = sum of all sides. The rhombus has equal sides, so its perimeter = side x 4.

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How can I find the height of a rhombus?

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In a rhombus, the diagonals bisect and are perpendicular, meaning that inside the rhombus there are four right-angle triangles, with side lengths half that of the diagonals, use the pythagoran theorem to find the hypotenuses a² + b² = c² Now we have the base, given any of the angles inside the rhombus, we can find all of them because they are corresponding and all add up to 360 degrees, once we have all of the angles, another two identical triangles appear. we only have to use one of these as they are identical. Now we have the hypotenuse and an angle of this triangle so using trigonometry we can find the adjacent side which is the height of the rhombus.

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How do I determine the perimeter given one diagonal and the area?

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Use the Pythagorean theorem to find the sides and then find the perimeter.

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