Última atualização: 19 de agosto de 2026
Área do Losango Calculadora
Criadores
Dharmendra SinghRevisores
Criadores
Dharmendra SinghRevisores
Quick Answer
A rhombus with diagonals d₁ and d₂ has area A = d₁d₂/2. This calculator also uses the right triangles formed by the half-diagonals to derive side length, perimeter, and height, making it useful for both quick geometry answers and hand-checked examples.
The area of a rhombus equals one-half the product of its two diagonals.
Pontos-Chave
- Rhombus area from diagonals is A = d₁d₂/2.
- Half-diagonals form right triangles.
- Those right triangles reveal the side length.
- Perimeter is four times the side length.
- Height can be recovered by dividing area by side length.
Criadores
Dharmendra SinghRevisores
Criadores
Dharmendra SinghRevisores
Fórmula
Area = (diagonal1 × diagonal2) ÷ 2
Onde:
- A=Area of the rhombus(square units)
- d_1=First diagonal(units)
- d_2=Second diagonal(units)
Exemplos resolvidos
Diagonals 10 and 24
A classic Pythagorean rhombus example.
- 1Use A = d₁d₂/2 = 10 × 24 / 2.
- 2That gives A = 120 square units.
- 3Half-diagonals 5 and 12 form a right triangle, so the side is 13 and the perimeter is 52.
Diagonals 12 and 16
A rhombus with a derived side of 10.
- 1Compute area: 12 × 16 / 2 = 96.
- 2Half-diagonals 6 and 8 give side length √(6² + 8²) = 10.
- 3Perimeter is 4 × 10 = 40.
Diagonals 14 and 48
Larger diagonals still use the same halved-diagonal triangle.
- 1Compute area: 14 × 48 / 2 = 336.
- 2Half-diagonals 7 and 24 produce side length 25.
- 3Perimeter is 100 and the height to that side is 336 ÷ 25 = 13.44.
Introdução
The Rhombus Area Calculator uses the diagonal formula A = d₁d₂ / 2 to find area quickly and accurately, then derives helpful supporting measures from the same geometry. Because the diagonals of a rhombus bisect each other at right angles, they also create right triangles that reveal side length, perimeter, and height. That makes the calculator useful for geometry homework, design sketches, and any problem where diagonals are known more readily than a base-and-height pair.
What rhombus area measures
The area of a rhombus is the amount of two-dimensional space enclosed by its four equal sides. When the diagonals are known, area is especially easy to compute because the formula uses only their product and a division by two.
Area is measured in square units.
A rhombus has four equal sides.
Its diagonals cross at right angles.
The diagonals bisect each other.
Why the diagonal formula works
A rhombus can be split into four right triangles by its diagonals. When those triangle areas are added together, the result simplifies to one-half of the product of the diagonals.
Use A = d₁d₂/2 for diagonal-based problems.
Half-diagonals form right triangles.
Those triangles help derive the side length.
The same geometry also gives perimeter and height.
Worked example
If the diagonals are 10 and 24, the area is 10 × 24 / 2 = 120. The half-diagonals are 5 and 12, so the side is √(5² + 12²) = 13, which makes the perimeter 52.
Multiply the diagonals first.
Divide by 2 for the area.
Halve each diagonal to build a right triangle.
Use the Pythagorean theorem for the side length.
Inputs and outputs
The calculator asks for the two diagonal lengths. From those values it returns the area directly and also computes the side length, perimeter, and the corresponding height measured against the derived side.
Both diagonals must be positive.
Area is the primary result.
Side length comes from the half-diagonal triangle.
Height follows from area ÷ side.
Common mistakes
A frequent error is forgetting the division by 2 in the area formula. Another is using the full diagonals instead of half-diagonals inside the Pythagorean theorem when deriving the side length.
Do not skip the divide-by-two step.
Do not use full diagonals in the right triangle.
Do not mix linear and square units.
Do not round too early if you still need height or perimeter.
Where this formula is used
People use rhombus area in tiling patterns, decorative layouts, drafting, and geometric design. In classroom settings it also provides a clean example of how symmetry and right triangles simplify area calculations.
Decorative floor or wall patterns.
Geometric art and tessellations.
Construction sketches and drafting problems.
Geometry lessons on diagonals and symmetry.
Manual method versus calculator use
The diagonal formula is simple enough to do by hand, but a calculator is helpful when the diagonals are decimals or when you also want supporting values such as perimeter and derived height. Estimating the answer first is still a smart accuracy check.
Area should scale with both diagonals.
Longer diagonals mean a larger area.
Use the calculator for decimal-heavy problems.
Keep the half-diagonal triangle in mind when checking side length.
Cartão de Referência Rápida
Rhombus area quick reference
Referência rápida • Área do Losango Calculadora
A = d₁d₂ / 2Faixa válida: Use positive diagonal lengths.
Valores Comuns
⚠ Cuidado
- •Do not forget to divide by 2.
- •Do not use full diagonals in the side-length triangle.
- •Do not mix units between diagonals.
- •Do not round before computing derived values if precision matters.
Dicas Pro
- →Draw the diagonals to visualize the right triangles.
- →Compute the area first because it is direct.
- →Use half-diagonals for the side length.
- →Check height by area ÷ side.
Perguntas Frequentes
What formula does the calculator use?
It uses A = d₁d₂ / 2, where d₁ and d₂ are the rhombus diagonals.
Why does dividing by 2 appear in the formula?
Because the diagonals split the rhombus into triangles whose combined area simplifies to half the product of the diagonals.
Can I find side length from the diagonals?
Yes. Use half of each diagonal as legs of a right triangle and apply the Pythagorean theorem.
What is the perimeter of a rhombus?
It is four times the side length, because all four sides are equal.
Is every square a rhombus?
Yes. A square is a special rhombus with four right angles and equal diagonals.
What if my diagonals are decimals?
The same formulas still work as long as the diagonal lengths are positive.
How can I check the height result?
Use height = area ÷ side after the side length has been derived from the half-diagonals.