Calculate the Area of a Rhombus

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

Steps

Using the Diagonals

  1. 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.
    • Let's say the diagonals are 6 cm. and 8 cm. long.
  2. Multiply the length of the diagonals. 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. Divide the result by 2. 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.

Using the Base and Height

  1. Find the base and the height. 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.
  2. Multiply the base and height. 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.

Using Trigonometry

  1. Square the length of any side. 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.
  2. Multiply it by the sine of one of the angles. 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.

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