## Rhombus-Geometry Formulas

### Rhombus

Rhombus is a special type of parallelogram whose all sides are equal. The angles between the sides of a rhombus need not be a right angle, and there it differs from a square, whose all angles are the right angle. Thus, a rhombus with right angles becomes square.

### The Perimeter of a Rhombus:

The perimeter is the sum of the length of all the 4 sides. In rhombus all sides are equal.

So, Perimeter of rhombus = 4 × side

P = 4s

### Area of Rhombus:

Area of a rhombus can be derived in 3 ways:<

1. Using diagonals – A = ½ × d1 × d2.
2. Using Base and Height – A = b × h.
3. Using trigonometry – A = b2 × Sin(a).

Where

• d1 = Length of diagonal 1.
• d2 = Length of diagonal 2.
• b = Length of any side.
• h = Height of rhombus.
• a = Measure of interior angle.

### Properties of Rhombus

1. In a rhombus all sides are equal
2. In a rhombus opposite angles are equal.
3. Also, in a rhombus the sum of adjacent angles are supplementary i.e. (∠B + ∠C = 180°).
4. In a rhombus, if one angle is right, then all angles are right.
5. In a rhombus, each diagonal of a rhombus divides it into two congruent triangles.
6. Diagonals of a rhombus bisect each other and also perpendicular to each other.