Buzz
A rhombus is a type of parallelogram where all four sides are of equal length. There are three methods to determine the area of a rhombus. Follow these steps:
Steps
Using Diagonals
Determine the length of each diagonal. The diagonals of a rhombus are the lines connecting opposite vertices. These diagonals intersect each other at right angles.
- For example, let’s assume the lengths of the two diagonals are 6 cm and 8 cm.
Multiply the lengths of the two diagonals. Simply measure and note down the lengths of the diagonals, then multiply them together. In this case, 6 cm x 8 cm = 48 cm2. Remember to use square units since this represents area.
Divide the result by 2. From the previous step, we have 6 cm x 8 cm = 48 cm2. Divide this number by 2. 48 cm2/2 = 24 cm2. Thus, the area of the rhombus is 24 cm2.
Using Base Length and Height
Determine the base length and height. Another method to calculate the area of a rhombus is by multiplying the length of one side by its corresponding height. For example, let’s assume the height is 7 cm and the base is 10 cm.
Multiply the base by the height. Once you know the base length and height of the rhombus, simply multiply them to find the area. Here, 10 cm x 7 cm = 70 cm2. The area of the rhombus is 70 cm2.
Using Trigonometric Formulas
Square the length of any side of the rhombus. Since all four sides of a rhombus are equal, you can choose any side. For example, if a side measures 2 cm, then 2 cm x 2 cm = 4 cm2.
Multiply the result by the sine of one of the angles; it doesn’t matter which angle you choose. Suppose one angle is 33 degrees. Multiply sin (33) by 4 cm2 to find the area of the rhombus. (2 cm)2 x sin (33) = 4 cm2 x 1 = 4 cm2. The area of the rhombus is 4 cm2.
