Understanding the Properties and Calculating the Area of a Rhombus | Step-by-Step Guide with Example

Rhombus

A rhombus is a quadrilateral with four sides of equal length

A rhombus is a quadrilateral with four sides of equal length. It is also known as a diamond shape. In a rhombus, opposite sides are parallel to each other, and opposite angles are equal.

Properties of a Rhombus:
1. All sides of a rhombus have the same length.
2. Opposite sides of a rhombus are parallel.
3. Opposite angles of a rhombus are equal.
4. Adjacent angles in a rhombus are supplementary (they add up to 180 degrees).
5. Diagonals of a rhombus bisect each other at right angles.
6. The diagonals of a rhombus are perpendicular bisectors of each other.
7. The area of a rhombus can be calculated as the product of its diagonals divided by 2: Area = (d1 x d2)/2, where d1 and d2 are the lengths of the diagonals.

To better understand some of these properties, let’s look at an example:

Example: Find the area of a rhombus with diagonals of length 8 cm and 10 cm.

Solution:
First, let’s label the given information. We have d1 = 8 cm and d2 = 10 cm.

To find the area of the rhombus, we can use the formula: Area = (d1 x d2)/2.

Substituting the given values, we have:
Area = (8 cm x 10 cm)/2 = 80 cm²/2 = 40 cm².

Therefore, the area of the rhombus is 40 cm².

Remember, when working with a rhombus, it is important to understand its properties and how they can be applied to different problems or calculations.

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