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# Rhombus calculator - diagonals, area, perimeter, sides

Rhombus calculator will help you calculate the long diagonal of the rhombus, the short diagonal of the rhombus, the side length, height, area of the rhombus, radius of the circle inscribed in the rhombus.

## Longer diagonal of the rhombus

### Longer diagonal of the rhombus from the side and angle

$$f=2a\cos {\tfrac {\alpha }{2}}$$

### Longer diagonal of the rhombus from the area and diagonal

$$f=\frac{2\cdot S }{d}$$

## Shorter diagonal of the rhombus

### Shorter diagonal of the rhombus from the side and the angle

$$d=2a\sin {\tfrac {\alpha }{2}}$$

### Shorter diagonal from area and diagonal

$$d=\frac{2\cdot S }{f}$$

## Height of the rhombus

### Height of the rhombus from the side and area

$$h=\frac{S}{a}$$

### Height of the rhombus from the angle and area

$$h=\sqrt{S\cdot \sin(\alpha)}$$

## Area of the rhombus

### Area from the side and height

$$S=a\cdot h$$

### Area from side and angle

$$S=a^{2}\cdot \sin \alpha =a^{2}\cdot \sin \beta$$

### Area from height and angle

$$S=\frac {h^{2}}{\sin \alpha }$$

### Area from diagonals

$$S=\frac {d\cdot f}{2}$$

### Area from the side and radius of the inscribed circle

$$S=2a\cdot r$$

## Perimeter of a Rhombus

$$L= 4\cdot a$$

### Radius of the circle inscribed in the rhombus from the side and angle

$$r={\tfrac {1}{2}}a\sin \alpha$$

### Radius of the circle inscribed in the rhombus from diagonals

$$r={\frac {d\cdot f}{2{\sqrt {d^{2}+f^{2}}}}}$$

Rhombus - information

Rhombus - a quadrilateral with sides of equal length; equivalently, a quadrilateral with mutually perpendicular and intersecting halves.
Each rhombus is a parallelogram and is also a deltoid. A special case of a rhombus is a square, which is a rhombus with right angles and at the same time is a rhombus with diagonals of the same length.

It has the following properties:
1. The rhombus is a convex figure.
2. The sum of the measures of all interior angles is 2 Π (360 °), and the sum of the measures of two adjacent interior angles is Π, $$\alpha + \beta = 180°$$ means: $$\alpha = 180° - \beta$$ $$\beta = 180° - \alpha$$
3. The diagonals intersect at right angles dividing the rhombus into four congruent right triangles.
4. The point of intersection of the rhombus diagonals divides each of them into two halves, marking the center of the inscribed circle being the center of symmetry of the rhombus.
5. The diagonals coincide with the bisectors of the angles and the symmetry axes of the rhombus.
6. Formula on the longer diagonal of the rhombus on the side and angle
7. $$f=2a\cos {\tfrac {\alpha }{2}}$$
8. Formula on the longer diagonal of the diamond from the area and the diagonal
9. $$f=\frac{2\cdot S }{d}$$
10. Formula for the shorter diagonal of the diamond on the side and angle
11. $$d=2a\sin {\tfrac {\alpha }{2}}$$
12. Formula for the shorter diagonal of the diamond from the area and the diagonal
13. $$d=\frac{2\cdot S }{f}$$
14. Formula for height of the rhombus from the side and the surface area
15. $$h=\frac{S}{a}$$
16. Formula for height of the rhombus from the angle and area
17. $$h=\sqrt{S\cdot \sin(\alpha)}$$
18. Wzór na Area from the side and height
19. $$S=a\cdot h$$
20. Formula for area from side and angle
21. $$S=a^{2}\cdot \sin \alpha =a^{2}\cdot \sin \beta$$
22. Formula for area from height and angle
23. $$S=\frac {h^{2}}{\sin \alpha }$$
24. Formula for area from diagonals
25. $$S=\frac {d\cdot f}{2}$$
26. Formula for area from the side and radius of the inscribed circle
27. $$S=2a\cdot r$$
28. Formula for perimeter of a Rhombus
29. $$L= 4\cdot a$$
30. Formula for radius of the circle inscribed in the rhombus from the side and angle
31. $$r={\tfrac {1}{2}}a\sin \alpha$$
32. Formula for radius of the circle inscribed in the rhombus from diagonals
33. $$r={\frac {d\cdot f}{2{\sqrt {d^{2}+f^{2}}}}}$$

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