The area of a rhombus helps us understand how much surface the shape covers. Since a rhombus looks like a tilted square with all sides equal, its area can be calculated using either its diagonals or its side with the angle between them. These formulas are widely used in geometry, land measurement, design work, and competitive exams.
Formula for Calculating the Area of a Rhombus Overview
| Formula | Variables & Meaning | When it is Used |
|---|---|---|
| Area = (d₁ × d₂) ÷ 2 | d₁ = first diagonal, d₂ = second diagonal | When diagonals are known |
| Area = a² × sin θ | a = side of the rhombus, θ = angle between adjacent sides | When side and angle are given |
What is the Area of a Rhombus in Maths?
In mathematics, the area of a rhombus represents the total region enclosed within its four equal sides. Since the diagonals of a rhombus intersect at right angles, they divide the shape into four right-angled triangles, making it easy to calculate its area using diagonals.
There are two main ways to calculate the area:
1. Using diagonals – Multiply the lengths of the diagonals and divide by 2.
2. Using side and angle – If diagonals are not known, apply the formula a² × sin θ, where θ is the angle between the sides.
These formulas are extremely useful in everyday applications like tiling, land measurement, diamond-shaped patterns, and also in exams like CUET, JEE, SSC, Banking, and school geometry.
Examples to Calculate Area of a Rhombus
Example 1: Diagonals = 12 cm and 8 cm
Step 1: Area = (d₁ × d₂) ÷ 2
Step 2: Area = (12 × 8) ÷ 2
Step 3: Area = 96 ÷ 2
Result: 48 cm²
So, the area of the rhombus is 48 cm².
Example 2: Side = 10 cm and Angle = 60°
Step 1: Area = a² × sin θ
Step 2: Area = 10² × sin(60°)
Step 3: Area = 100 × 0.866
Result: 86.6 cm²
So, the area of the rhombus is 86.6 cm².
FAQs about Area of a Rhombus Formula
Q1. What is the area of a rhombus?
It is the total space enclosed by the rhombus, measured in square units like cm² or m².
Q2. Are diagonals necessary to calculate the area?
No, you can also use the side length and the angle between the sides.
Q3. Is every rhombus a square?
No. Every square is a rhombus, but a rhombus becomes a square only when all angles are 90°.
Q4. Why do the diagonals intersect at right angles?
It is a geometric property of rhombuses, making the area calculation easier.
Q5. Where is this area formula used in real life?
In agriculture, construction, tiling, design patterns, and competitive exam problems.
Q6. Can area ever be negative?
No, because area represents physical surface space, it is always positive.