Key Properties and Formulae of Rhombus | Understanding the Characteristics and Calculations of a Rhombus

Rhombus

A rhombus is a quadrilateral (a polygon with four sides) that has several unique characteristics

A rhombus is a quadrilateral (a polygon with four sides) that has several unique characteristics. It is a special type of parallelogram, which means that opposite sides are parallel and congruent (equal in length).

Key Properties of a Rhombus:
1. All sides of a rhombus are congruent. This means that each side has the same length.
2. Opposite angles in a rhombus are congruent. This means that the angles formed by connecting opposite vertices (corners) are equal in measurement.
3. Adjacent angles in a rhombus are supplementary. This means that the sum of any two adjacent angles is always equal to 180 degrees.
4. Diagonals of a rhombus bisect each other. This means that the diagonals (lines connecting opposite vertices) intersect at their midpoints, dividing each diagonals into two equal segments.
5. The diagonals of a rhombus are perpendicular. This means that the diagonals intersect at a right angle (90 degrees).
6. The diagonals of a rhombus are also angle bisectors. This means that the diagonals divide each angle into two equal parts.

Formulae for a Rhombus:
1. Area: The area of a rhombus can be calculated using the formula A = (d₁ * d₂)/2, where d₁ and d₂ represent the lengths of the diagonals.
2. Perimeter: The perimeter of a rhombus is simply the sum of the lengths of all four sides.

Example:
Let’s consider a rhombus with side length 6 units and diagonals measuring 10 units and 8 units.

1. Area: A = (d₁ * d₂)/2 = (10 * 8)/2 = 40 square units.
2. Perimeter: P = 4 * side length = 4 * 6 = 24 units.

So, the area of the rhombus is 40 square units, and its perimeter is 24 units.

I hope this helps! Let me know if you have any further questions.

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