Area of a rhombus calculator
Diagonals of 6 and 8 give 24 square units in the area of a rhombus calculator, with sides of 5 and a perimeter of 20.
Area
- Area
- 24 square units
- Formula
- A = (d1 x d2) / 2 = (6 x 8) / 2
- Perimeter Four equal sides: 4s.
- 20
- Side length The hypotenuse of a right triangle with legs of half each diagonal: sqrt(3^2 + 4^2).
- 5
- Angles Opposite angles are equal and neighboring angles add to 180 degrees. The larger angle sits at the ends of the shorter diagonal.
- 106.26 and 73.74 degrees
- Height Area divided by the side: the perpendicular distance between two opposite sides.
- 4.8
- If the units were feet
- 24 sq ft = 2.6666667 sq yd = 0.0005509642 acres
- Doubling every length
- 96 square units
How the Area Calculator works
The area of rhombus formula uses the two diagonals: A = (d₁ × d₂) ÷ 2. The diagonals of a rhombus cross at right angles and cut each other in half, so they split it into four identical right triangles, which together fill half of the rectangle d₁ by d₂.
Worked example: diagonals of 6 and 8. A = 6 × 8 ÷ 2 = 24 square units. Each of the four right triangles has legs of half the diagonals, 3 and 4, so its hypotenuse, the side of the rhombus, is √(3² + 4²) = 5.
All four sides of a rhombus are equal, so the perimeter of rhombus formula is P = 4s, here 4 × 5 = 20. From the diagonals alone, s = √((d₁ ÷ 2)² + (d₂ ÷ 2)²).
A rhombus is a parallelogram with equal sides, so base times height works as well. The height is the area divided by the side, 24 ÷ 5 = 4.8, and 5 × 4.8 = 24. With the side and an interior angle instead, A = s² sin θ. The angles of this rhombus are 106.26° and 73.74°, and 5² × sin 73.74° = 24.
Opposite angles of a rhombus are equal and neighboring angles add to 180°, so one angle fixes all four. A square is the rhombus whose angles are all 90°: its diagonals are equal, and (d × d) ÷ 2 gives a square's area from its diagonal.
Area Calculator FAQ
How do I find the area of a rhombus from the side and an angle?
Multiply the side squared by the sine of either interior angle: A = s² sin θ. A rhombus with sides of 10 and a 30° angle has 100 × 0.5 = 50 square units. Both angles give the same answer, because sin θ = sin(180° - θ).
How do I find a diagonal from the area?
Rearrange A = d₁ × d₂ ÷ 2 to d₂ = 2A ÷ d₁. A rhombus of 24 square units with one diagonal of 6 has the other diagonal 2 × 24 ÷ 6 = 8.
What is the difference between a rhombus and a parallelogram?
Every rhombus is a parallelogram whose four sides are all equal. Equal sides are what make the diagonals cross at right angles, which a general parallelogram's do not, so the diagonal formula works for a rhombus and not for other parallelograms.