Summary of Quadrilateral: Rhombus

Goals

1. Understand the characteristics of a rhombus.

2. Calculate the lengths of sides and angles in a rhombus.

3. Solve problems related to rhombuses by recognising their unique properties.

Contextualization

Rhombuses are geometric shapes we often see in our daily surroundings, like in floor tile designs, fabric patterns, and even logos of businesses. Learning about the properties of rhombuses not only boosts our mathematical abilities but is also fundamental in practical scenarios, such as calculating area and perimeter in different contexts. For instance, in building design, getting the measurements right for rhombuses is vital to ensure optimal use of materials and reduce wastage.

Subject Relevance

To Remember!

Definition of Rhombus

A rhombus is a type of quadrilateral where all sides are of equal length. Also, an important aspect of rhombuses is that their opposite angles are equal, meaning they measure the same.

• A rhombus is a quadrilateral with all sides being equal.

• The opposite angles of a rhombus are the same.

• Rhombuses can be regarded as a specific variety of parallelogram.

Properties of Rhombuses

The key properties of rhombuses include the equality of the four sides and the equality of opposite angles. Additionally, the diagonals of a rhombus cross each other at right angles (90°) and bisect one another.

• All sides of a rhombus are equal in length.

• The diagonals of a rhombus meet at right angles.

• The diagonals of a rhombus bisect one another.

Calculating Internal Angles and Perimeter

To find the internal angles of a rhombus, remember that the opposite angles are equal. The perimeter of a rhombus is simply the total length of its sides, which can be calculated by multiplying the length of one side by four.

• The sum of the internal angles of a rhombus is 360°.

• The opposite angles of a rhombus are equal.

• The perimeter of a rhombus is four times the length of one side.

Practical Applications

• In architecture, rhombuses are often incorporated into floor layouts and façade designs to create aesthetically appealing and practical patterns.

• In interior decoration, rhombuses can enhance carpets, curtains, and furniture upholstery, adding balance and style to spaces.

• In civil engineering, understanding rhombuses is vital for calculating areas and optimizing materials, especially in constructions that necessitate geometric accuracy and effective resource management.

Key Terms

• Rhombus: A quadrilateral with all sides equal and opposite angles equal.

• Quadrilateral: A geometric figure with four sides and four angles.

• Diagonals: The line segments joining opposite corners of a polygon.

• Perimeter: The total length of all sides of a geometric figure.

• Internal Angles: Angles formed between adjacent sides of a polygon.

Questions for Reflections

• How can we use our understanding of rhombus properties in architectural projects to minimize material wastage?

• In what ways can knowing how to calculate the perimeters and areas of rhombuses be helpful in our everyday lives or future professions?

• What difficulties did you face while creating a 3D model of a rhombus, and how did you manage to tackle them?

Practical Challenge: Rhombus in Action

Design a floor pattern using cut-out cardboard rhombuses.

Instructions

• Cut out 10 cardboard rhombuses, each with a side length of 5 cm.

• Arrange them to create a continuous and symmetrical design.

• Measure the total perimeter of the created pattern.

• Calculate the area covered by the rhombus pattern.

• Take a picture of your final design and include your measurements and calculations in a report.