102 LearnersLast updated on August 30, 2025
Surface Area of Rhombus
A rhombus is a 2-dimensional quadrilateral with all sides having equal length. The surface area of a rhombus refers to the total area enclosed by its boundaries. In this article, we will learn about the surface area of a rhombus.
What is the Surface Area of a Rhombus?
The surface area of a rhombus is the total area enclosed within its four sides. It is measured in square units.
A rhombus is a type of polygon that is essentially a parallelogram with equal-length sides.
It can be thought of as a "tilted square.
" The opposite angles of a rhombus are equal, and the diagonals intersect at right angles.
There are two primary methods to calculate the surface area of a rhombus, depending on the known dimensions.
Surface Area of a Rhombus Formula
The surface area of a rhombus can be calculated using different formulas depending on the given parameters.
The common formulas involve the lengths of the diagonals or the base and height of the rhombus.
Below are the formulas for calculating the surface area of a rhombus:
Surface Area Using Diagonals
The area of a rhombus can be calculated using its diagonals. If the lengths of the diagonals are known, the formula to calculate the surface area is:
Surface Area = (d1 × d2) / 2 square units
Here, d1 and d2 are the lengths of the diagonals of the rhombus.
Surface Area Using Base and Height
If the base and the perpendicular height of a rhombus are known, the surface area can be calculated using the following formula:
Surface Area = base × height square units
Where the base is the length of one side of the rhombus and the height is the perpendicular distance between two opposite sides.
Perimeter of a Rhombus
The perimeter of a rhombus is the total length of its outer boundary, which is simply four times the length of one side. The formula for calculating the perimeter is: Perimeter = 4 × side length
Mixing Up Diagonal and Side Lengths
Students sometimes confuse the diagonal lengths with the side lengths. Always remember that the diagonal is the line connecting two opposite corners, while the side is the length of the rhombus's boundary.
Mistake 1
Using Wrong Formula
Ensure you use the correct formula based on the given dimensions. If you have the diagonals, use the diagonal formula, and if you have the base and height, use the base-height formula.
Mistake 2
Forgetting to Halve the Product of Diagonals
A common mistake is forgetting to divide the product of the diagonals by 2 when using the diagonal formula. The correct formula is (d1 × d2) / 2.
Mistake 3
Not Using Perpendicular Height
When using the base-height formula, make sure the height used is perpendicular to the base. Using any other length may lead to incorrect results.
Mistake 4
Assuming All Quadrilaterals with Equal Sides Are Squares
A rhombus is not necessarily a square; it is a parallelogram with equal sides. The angles are not necessarily right angles unless specified.
Mistake 5
Solved Examples of Surface Area of Rhombus
Find the surface area of a rhombus with diagonals of 10 cm and 8 cm.
Surface Area = 40 cm²
Problem 1
Using the formula: Surface Area = (d1 × d2) / 2 = (10 × 8) / 2 = 80 / 2 = 40 cm²
Find the surface area of a rhombus with a base of 12 cm and a height of 7 cm.
Explanation
Surface Area = 84 cm²
Problem 2
Using the formula: Surface Area = base × height = 12 × 7 = 84 cm²
The diagonals of a rhombus are 16 cm and 12 cm. Find the surface area.
Explanation
Surface Area = 96 cm²
Problem 3
Using the formula: Surface Area = (d1 × d2) / 2 = (16 × 12) / 2 = 192 / 2 = 96 cm²
A rhombus has a side length of 10 cm and a height of 8 cm. Find the surface area.
Explanation
Surface Area = 80 cm²
Problem 4
Using the formula: Surface Area = base × height = 10 × 8 = 80 cm²
If a rhombus has diagonals measuring 14 cm and 9 cm, what is its surface area?
Explanation
Surface Area = 63 cm²
It is the total area enclosed by the four sides of the rhombus, calculated using either the diagonals or the base and height.
1.Can the surface area of a rhombus be negative?
2.How are the diagonals of a rhombus related?
3.What is the formula for the perimeter of a rhombus?
4.In what units is the surface area measured?
Common Mistakes and How to Avoid Them in the Surface Area of a Rhombus
Students often make mistakes while calculating the surface area of a rhombus, which leads to wrong answers. Below are some common mistakes and the ways to avoid them.
Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
