Rhombus Calculator
Calculate the area, perimeter, and side length of a rhombus using its diagonals.
Rhombus Dimensions
Diagonals are perpendicular
Results:
Area: 0.00 square units
Side: 0.0000 units
Perimeter: 0.0000 units
Step-by-Step Solution:
About Rhombuses
What is a Rhombus?
A rhombus is a parallelogram with all four sides equal in length. Its diagonals are perpendicular and bisect each other. A square is a special case of a rhombus with right angles.
Key Properties
- All four sides are equal in length
- Opposite angles are equal
- Diagonals are perpendicular (meet at 90°)
- Diagonals bisect each other
- Diagonals bisect the vertex angles
- Opposite sides are parallel
Formulas
Area: A = (d₁ × d₂) / 2
Perimeter: P = 4s (where s is the side length)
Side from Diagonals: s = √((d₁/2)² + (d₂/2)²)
Real-World Applications
- Jewelry: Diamond shapes, earring designs, gem cuts
- Design: Logos, kite designs, decorative patterns
- Architecture: Floor tiles, window patterns, lattice structures
- Traffic: Diamond-shaped road signs
- Sports: Baseball diamond layout
Frequently Asked Questions
What's the difference between a rhombus and a square?
A square is a special rhombus where all angles are 90°. Every square is a rhombus, but not every rhombus is a square. A rhombus can have any angle (as long as opposite angles are equal).
Why do the diagonals have to be perpendicular?
The perpendicular diagonals are a defining property of rhombuses. This property ensures that all four sides remain equal in length and creates four congruent right triangles.
How do I find the side length from diagonals?
Use the Pythagorean theorem. Each diagonal divides the rhombus into triangles. The side is the hypotenuse: side = √((d₁/2)² + (d₂/2)²).
Are the diagonals of a rhombus equal?
Not always. The diagonals are equal only when the rhombus is also a square. In a general rhombus, the diagonals have different lengths but are always perpendicular.
Is a rhombus a parallelogram?
Yes! A rhombus is a special type of parallelogram where all sides are equal. It has all the properties of a parallelogram plus equal sides and perpendicular diagonals.
What angles does a rhombus have?
Opposite angles are equal, and consecutive angles are supplementary (add to 180°). The angles can be any value as long as these properties hold. In a square, all angles are 90°.
How do diagonals bisect the angles?
Each diagonal splits the vertex angles into two equal parts. If a vertex angle is 60°, the diagonal divides it into two 30° angles.
Can I calculate area if I only know the side?
You also need an angle or one diagonal. With side and angle: A = s² × sin(θ). With side and one diagonal, you can find the other diagonal first.
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