Rhombus Calculator
Calculate rhombus area, perimeter, diagonals, angles, and height. Enter side and angle or diagonals to get all measurements with interactive visualization.
A = (d1 x d2) / 2 | P = 4aRhombus Properties
Area
86.6025 cm^2
Rhombus Input
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Rhombus Visualization
Diagonals bisect each other at right angles (90 degrees)
Complete Results
Side (a)
10.0000 cm
All sides equal
Acute Angle
60.00deg
Obtuse Angle
120.00deg
Diagonal 1 (longer)
17.3205 cm
Diagonal 2 (shorter)
10.0000 cm
Area
86.6025 cm^2
A = (d1 x d2) / 2
Perimeter
40.0000 cm
P = 4a
Height
8.6603 cm
h = Area / side
Inscribed Circle Radius
4.3301 cm
r = h / 2
Rhombus Formulas
Area Formulas
- A = (d1 x d2) / 2
- A = a^2 x sin(angle)
- A = base x height
Side & Diagonal Relations
- a = sqrt((d1/2)^2+(d2/2)^2)
- d1^2 + d2^2 = 4a^2
- P = 4a
Key property: The diagonals of a rhombus bisect each other at right angles (90 degrees), forming four congruent right triangles.
Rhombus Properties
Area
86.6025 cm^2
?How to Calculate Rhombus Properties
Rhombus formulas: All four sides are equal. Area = (d1 x d2) / 2 using diagonals, or Area = side squared x sin(angle). Perimeter = 4 x side. The diagonals bisect each other at right angles. Side can be calculated from diagonals: side = sqrt((d1/2)^2 + (d2/2)^2).
What is a Rhombus?
A rhombus (also called a diamond) is a quadrilateral with all four sides equal in length. It is a special type of parallelogram. The diagonals of a rhombus bisect each other at right angles (90 degrees) and also bisect the vertex angles. Opposite angles are equal, and consecutive angles are supplementary. A square is a special rhombus where all angles are 90 degrees.
Key Facts About Rhombi
- All four sides are equal in length
- Area = (d1 x d2) / 2 using both diagonals
- Area = a^2 x sin(angle) using side and angle
- Perimeter = 4a (four times the side)
- Diagonals bisect each other at 90 degrees
- Diagonals bisect the vertex angles
- Opposite angles are equal
- Consecutive angles are supplementary (sum to 180 degrees)
- Side = sqrt((d1/2)^2 + (d2/2)^2) from diagonals
- A square is a special rhombus with 90 degree angles
Quick Answer
Rhombus formulas: All four sides are equal. Area = (d1 x d2) / 2 using diagonals, or Area = side squared x sin(angle). Perimeter = 4 x side. The diagonals bisect each other at right angles. Side can be calculated from diagonals: side = sqrt((d1/2)^2 + (d2/2)^2).
Rhombus Practice Problems
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Practice with 4 problems to test your understanding.
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Frequently Asked Questions
The area of a rhombus can be calculated as: Area = (d1 x d2) / 2 using both diagonals, or Area = side^2 x sin(angle) using the side and one of the angles.
Since the diagonals bisect each other at right angles, each forms a right triangle with half of each diagonal. Use: side = sqrt((d1/2)^2 + (d2/2)^2).
The diagonals of a rhombus: (1) bisect each other at right angles (90 degrees), (2) bisect the vertex angles, and (3) divide the rhombus into four congruent right triangles.
A rhombus is also a square when all four angles are right angles (90 degrees). This happens when both diagonals are equal in length.
Opposite angles of a rhombus are equal. Consecutive angles are supplementary (sum to 180 degrees). If one angle is A, the adjacent angle is (180-A).
The inscribed circle (incircle) of a rhombus has radius r = Area / (perimeter/2) = Area / (2s) = height / 2, where s is the side length.
Last updated: 2025-01-15
Rhombus Properties
Area
86.6025 cm^2