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Diagonals
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Results are also pinned to the bottom of your screen.Rhombus Properties
Area
24
square units
Perimeter
20
units
Formulas Used
Area = (d1 × d2) / 2 = (6 × 8) / 2 = 24Side = √((d1/2)² + (d2/2)²) = 5Perimeter = 4 × side = 20Acute angle = 2 × arctan(min(d1,d2) / max(d1,d2)) = 73.7398° (obtuse = 180° − acute)
Quick Answer
To calculate rhombus properties from two diagonals: Area = (d1 x d2) / 2, side = sqrt((d1/2)^2 + (d2/2)^2), Perimeter = 4 x side. For diagonals 6 and 8: Area = 24 square units, side = 5, Perimeter = 20 units, angles of 73.74 and 106.26 degrees. Alternative input with a side and angle: Area = side^2 x sin(angle).
Key Facts
- Formula: Area = (d1 x d2) / 2 (half the product of the diagonals)
- Formula: Perimeter = 4 x side
- Formula: Area = side^2 x sin(angle) when a side and angle are known
- Diagonals 6 and 8 give area 24, side 5, perimeter 20
- The diagonals of a rhombus always bisect each other at 90 degrees
- All four sides of a rhombus are equal; opposite angles are equal
- A square is a rhombus with 90-degree angles
Frequently Asked Questions
How do I calculate the area of a rhombus?
From the two diagonals: Area = (d1 x d2) / 2. Diagonals 6 and 8 give area 24 square units. From a side and angle: Area = side^2 x sin(angle). Both formulas always agree for the same rhombus.
How do I find the side of a rhombus from its diagonals?
The diagonals bisect each other at right angles, so each side is the hypotenuse of a right triangle with legs d1/2 and d2/2: side = sqrt((d1/2)^2 + (d2/2)^2). Diagonals 6 and 8 give side = sqrt(9 + 16) = 5.
What is the perimeter of a rhombus?
All four sides are equal, so Perimeter = 4 x side. With side 5, the perimeter is 20 units. From the diagonals, first compute the side with the Pythagorean theorem, then multiply by 4.
Do the diagonals of a rhombus cross at right angles?
Yes. This is the defining property that makes the area formula work: the diagonals split the rhombus into four congruent right triangles, each with area (d1/2)(d2/2)/2, totaling (d1 x d2)/2.
What is the difference between a rhombus and a square?
A rhombus requires four equal sides; a square adds four 90-degree angles. Every square is a rhombus, but a rhombus is only a square when its angles are all right angles (equivalently, when d1 = d2).
How do I find the angles of a rhombus?
From the diagonals, the angle at the vertex where d1 meets the side follows from arctan(d2/d1); the full interior angle is 2 x arctan(d2/d1) or its supplement. Diagonals 6 and 8 give angles of 73.74 and 106.26 degrees. From a side and one angle, the opposite angle is equal and adjacent angles sum to 180.